{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 18 An Introduction to Graph Theory and Network Analysis\n",
    "## 18. 1 Using Basic Graph Theory to Rank Websites by Popularity\n",
    "\n",
    "lets build a simple network composed of two data science websites; _NumPy_ and _Scipy_.  In graph theory, these websites are referred to as the *nodes* within the graph. Nodes are network points which can form connections with each other. \n",
    "\n",
    "**Listing 18. 1. Defining a node list**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = ['NumPy', 'SciPy']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose the _SciPy_ website is discussing NumPy dependencies. This discussion includes a web-link to the _NumPy_ page. We'll treat this connection as an edge that goes from index 1 to index 0. The edge can be expressed as the tuple `(1, 0)`. \n",
    "\n",
    "**Listing 18. 2. Defining an edge list**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges = [(1, 0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given our directed `edges` list, we can easily check if a webpage at index `i` links a webpage at index `j`. That connection exists if `(i, j) in edges` equals `True`.\n",
    "\n",
    "**Listing 18. 3. Checking for the existence of an edge**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def edge_exists(i, j): return (i, j) in edges\n",
    "\n",
    "assert edge_exists(1, 0)\n",
    "assert not edge_exists(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our `edge_exists` function works, but it's not efficient. The function must traverse a list to check the presence of an edge. One alternative approach is to store the presence or absence of each edge `(i, j)` within the ith row and jth column of a matrix. This matrix representation of a network is known as an **adjacency matrix**. \n",
    "\n",
    "\n",
    "**Listing 18. 4. Tracking nodes and edges using a matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "adjacency_matrix = np.zeros((len(nodes), len(nodes)))\n",
    "for i, j in edges:\n",
    "    adjacency_matrix[i][j] = 1\n",
    "    \n",
    "assert adjacency_matrix[1][0]\n",
    "assert not adjacency_matrix[0][1]\n",
    "\n",
    "print(adjacency_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our matrix print-out permits us to view those edges that are present in the network. Additionally, we can observe potential edges that are missing from the network. Lets turn our attention to the missing edge going from _Node 0_ to _Node 1_. We'll add that edge to our adjacency matrix. This will imply that the _NumPy_ page now links to the _SciPy_ page.\n",
    "\n",
    "**Listing 18. 5. Adding an edge to the adjacency matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1.]\n",
      " [1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "adjacency_matrix[0][1] = 1\n",
    "print(adjacency_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we wish to expand our website network by adding two more data science sites. We'll need to expand the adjacency matrix dimensions from 2-by-2 to 4-by-4. Unfortunately, in NumPy, it's quite hard to resize a matrix while maintaining all existing matrix values.  We need to switch to a different Python library; NextworkX.\n",
    "\n",
    "### 18.1.1 Analyzing Web Networks Using NetworkX\n",
    "\n",
    "We'll begin by installing NetworkX. Afterwords, we'll import `networkx` as `nx`, per the common NetworkX usage convention.\n",
    "\n",
    "**Listing 18. 6. Importing the NetworkX library**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will utilize `nx` to generate a directed graph. In NetworkX, directed graphs are tracked using the `nx.DiGraph` class.\n",
    "\n",
    "**Listing 18. 7. Initializing a directed graph object**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.DiGraph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets slowly expand the directed graph. To start, we'll add a single node.\n",
    "\n",
    "**Listing 18. 8. Adding a single node to a graph object**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.]]\n"
     ]
    }
   ],
   "source": [
    "G.add_node(0)\n",
    "print(nx.to_numpy_array(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our single node is associated with a _NumPy_ webpage. We can explicitly record this association by executing `G.nodes[0]['webpage'] = 'NumPy'`. \n",
    "\n",
    "\n",
    "**Listing 18. 9. Adding an attribute to an existing node**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The attribute dictionary at node 0 is {}\n",
      "\n",
      "We've added a webpage to node 0\n",
      "The attribute dictionary at node 0 is {'webpage': 'NumPy'}\n"
     ]
    }
   ],
   "source": [
    "def print_node_attributes():\n",
    "    for i in G.nodes:\n",
    "        print(f\"The attribute dictionary at node {i} is {G.nodes[i]}\")\n",
    "\n",
    "print_node_attributes()\n",
    "G.nodes[0]['webpage'] = 'NumPy'\n",
    "print(\"\\nWe've added a webpage to node 0\")\n",
    "print_node_attributes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've added a node attribute after first inserting the node into the graph. However, we can also assign attributes directly while inserting a node into the graph.\n",
    "\n",
    "**Listing 18. 10. Adding a node with an attribute**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The attribute dictionary at node 0 is {'webpage': 'NumPy'}\n",
      "The attribute dictionary at node 1 is {'webpage': 'SciPy'}\n"
     ]
    }
   ],
   "source": [
    "G.add_node(1, webpage='SciPy')\n",
    "print_node_attributes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Please note that we can output all the nodes and together with their attributes simply by running `G.nodes(data=True)`.\n",
    "\n",
    "**Listing 18. 11. Outputting nodes together with their attributes**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, {'webpage': 'NumPy'}), (1, {'webpage': 'SciPy'})]\n"
     ]
    }
   ],
   "source": [
    "print(G.nodes(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets add a web-link from _Node 1_ (SciPy) to _Node 0_ (NumPy). \n",
    "\n",
    "**Listing 18. 12. Adding a single edge to a graph object**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "G.add_edge(1, 0)\n",
    "print(nx.to_numpy_array(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Printing the adjacency matrix has given us a visual representation of the network. Unfortunately, our matrix visualization will grow cumbersome as other nodes are added.  What if instead, we plotted the network directly? Our two nodes could be plotted as two points in 2D space. Meanwhile, our single edge could be plotted as a line segment that connects these points. \n",
    "\n",
    "**Listing 18. 13. Plotting a graph object**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEuCAYAAADx63eqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAMOElEQVR4nO3dQWicZR7H8f+0CUlFh7JaUNpCD8VGUAstLN6sB6P04qWCLF7dQ2UvS/cgvQjSy+JVD/a0ICwLve1SaPdgPdmLggprlMIKZlGJQh0LTUya2UNMiW0zncy8877P+zyfz7HN+/Lk9OM7k3mn0+/3+wEAhdjV9AEAoE6GD4CiGD4AimL4ACiK4QOgKIYPgKIYPgCKYvgAKIrhA6Aohg+Aohg+AIpi+AAoiuEDoCiGD4CiGD4AimL4ACiK4QOgKIYPgKIYPgCKYvgAKIrhA6Aohg+Aokw1fYBh/XBjJS58vBgL3/Wit7wW3dmpmHu0Gy8fPxAPPzjT9PEAaIlOv9/vN32IQT795nq8c+VafPjVUkRErKyt3/6/2ald0Y+IE0f2xelnD8fRg3ubOSQArZH08L1/9es4d3EhltduxaBTdjoRs1O74+zJuXj1mUO1nQ+A9kn2pc6N0fsibq6u3/dn+/2Im6u34tzFLyIijB8A20ryj1s+/eZ6nLu4MNTobXVzdT3OXVyIzxavT+ZgALReksP3zpVrsbx2a6Rrl9duxbtXrlV8IgBykdzw/XBjJT78amnge3qD9PsRH3y5FD/eWKn2YABkIbnhu/Dx4tj36ETEhU/Gvw8A+Ulu+Ba+6/3mIwujWF5bj4Vvf67oRADkJLnh6y2vVXSf1UruA0Bekhu+7mw1n7Dozk5Xch8A8pLc8M092o2ZqfGONTu1K+Yee6iiEwGQk+SG79TxA2Pfox8Rp46Nfx8A8pPc8D3y4Ew8+/i+6HRGu74TEU/+rhPrN3uR8NPYAGhIcsMXEfH6icMxO7V7tItvrca//vqn2L9/f8zMzMTBgwfjrbfeqvaAALRWksN39ODeOHtyLvZM7+x4e6Z3xV+ePxy7ri/G6upqrK6uxtLSUuzfv39CJwWgbZIcvoiNB02fPflE7Jnefd+XPTudiD3Tu+PsySfi9PNPxptvvhkPPPBAdH690PABsCnpryWKiPhs8Xq8e+VafPDlUnRi48Ppmza/j++5I/vi9InD8fSBvRER8csvv8ShQ4ei1+vFe++9F2+88Ua88MIL8fbbb0e3223k9wAgDckP36Yfb6zEhU8WY+Hbn6O3vBrd2emYe+yhOHXs3t/A/tFHH8VPP/0UL774YvR6vThz5kxcunQpzp8/H/Pz8w38BgCkoDXDV4XLly/Ha6+9pv4ACpbse3yTMD8/H59//nlERDz11FNx+fLlhk8EQN2KKr6t1B9AmYoqvq3UH0CZii2+rdQfQDmKLb6t1B9AORTfHdQfQN4U3x3UH0DeFN8A6g8gP4pvAPUHkB/FNyT1B5AHxTck9QeQB8U3AvUH0F6KbwTqD6C9FN+Y1B9Auyi+Mak/gHZRfBVSfwDpU3wVUn8A6VN8E6L+ANKk+CZE/QGkSfHVQP0BpEPx1UD9AaRD8dVM/QE0S/HVTP0BNEvxNUj9AdRP8TVI/QHUT/ElQv0B1EPxJUL9AdRD8SVI/QFMjuJLkPoDmBzFlzj1B1AtxZc49QdQLcXXIuoPYHyKr0XUH8D4FF9LqT+A0Si+llJ/AKNRfBlQfwDDU3wZUH8Aw1N8mVF/AIMpvsyoP4DBFF/G1B/A3RRfxtQfwN0UXyHUH8AGxVcI9QewQfEVSP0BJVN8BVJ/QMkUX+HUH1AaxVc49QeURvFxm/oDSqD4uE39ASVQfNyT+gNypfi4J/UH5ErxcV/qD8iJ4uO+1B+QE8XHjqg/oO0UHzui/oC2U3yMTP0BbaT4GJn6A9pI8VEJ9Qe0heKjEuoPaAvFR+XUH5AyxUfl1B+QMsXHRKk/IDWKj4lSf0BqFB+1UX9AChQftVF/QAoUH41Qf0BTFB+NUH9AUxQfjVN/QJ0UH41Tf0CdFB9JUX/ApCk+kqL+gElTfCRL/QGToPhIlvoDJkHx0QrqD6iK4qMV1B9QFcVH66g/YByKj9ZRf8A4FB+tpv6AnVJ8tJr6A3ZK8ZEN9QcMQ/GRDfUHDEPxkSX1B2xH8ZEl9QdsR/GRPfUHbKX4yJ76A7ZSfBRF/QGKj6KoP0DxUSz1B2VSfBRL/UGZFB+E+oOSKD4I9QclUXxwB/UHeVN8cAf1B3lTfDCA+oP8KD4YQP1BfhQfDEn9QR4UHwxJ/UEeFB+MQP1Beyk+GIH6g/ZSfDAm9QftovhgTOoP2kXxQYXUH6RP8UGF1B+kT/HBhKg/SJPigwlRf5AmxQc1UH+QDsUHNVB/kA7FBzVTf9AsxQc1U3/QLMUHDVJ/UD/FBw1Sf1A/xQeJUH9QD8UHiVB/UA/FBwlSfzA5ig8SpP5gchQfJE79QbUUHyRO/UG1FB+0iPqD8Sk+aBH1B+NTfNBS6g9Go/igpdQfjEbxQQbUHwxP8UEG1B8MT/FBZtQfDKb4IDPqDwZTfJAx9Qd3U3yQMfUHd1N8UAj1BxsUHxRC/cEGxQcFUn+UTPFBgdQfJVN8UDj1R2kUHxRO/VEaxQfcpv4ogeIDblN/lEDxAfek/siV4gPuSf2RK8UH3Jf6IyeKD7gv9UdOFB+wI+qPtlN8wI6oP9pO8QEjU3+0keIDRqb+aCPFB1RC/dEWig+ohPqjLRQfUDn1R8oUH1A59UfKFB8wUeqP1Cg+YKLUH6lRfEBt1B8pUHxAbdQfKVB8QCPUH01RfEAj1B9NUXxA49QfdVJ8QOPUH3VSfEBS1B+TpviApKg/Jk3xAclSf0yC4gOSpf6YBMUHtIL6oyqKD2gF9UdVFB/QOuqPcSg+oHXUH+NQfECrqT92SvEBrab+2CnFB2RD/TEMxQdkQ/0xDMUHZEn9sR3FB2RJ/bEdxQdkT/2xleIDsqf+2ErxAUVRfyg+oCjqD8UHFEv9lUnxAcVSf2VSfACh/kqi+ABC/ZVE8QHcQf3lTfEB3EH95U3xAQyg/vKj+AAGUH/5UXwAQ1J/eVB8AENSf3lQfAAjUH/tpfgARqD+2kvxAYxJ/bWL4gMYk/prF8UHUCH1lz7FB1Ah9Zc+xQcwIeovTYoPYELUX5oUH0AN1F86FB9ADdRfOhQfQM3UX7MUH0DN1F+zFB9Ag9Rf/RQfQIPUX/0UH0Ai1F89FB9AItRfPRQfQILU3+QoPoAEqb/JUXwAiVN/1VJ8AIlTf9VSfAAtov7Gp/gAWkT9jU/xAbSU+huN4gNoKfU3GsUHkAH1NzzFB5AB9Tc8xQeQGfU3mOIDyIz6G0zxAWRM/d1N8QFkTP3dTfEBFEL9bVB8AIVQfxsUH0CBSq4/xQdQoJLrT/EBFK60+jN8AESv14szZ87EpUuX4vz58zE/Pz/w53+4sRIXPl6Mhe960Vtei+7sVMw92o2Xjx+Ihx+cqenUozF8ANx2v/r79Jvr8c6Va/HhV0sREbGytn77/2andkU/Ik4c2Rennz0cRw/urfHkw/MeHwC3DXrv7/2rX8cr56/Gv7/4PlbW1n8zehERy7/+2+X/fB+vnL8a71/9us6jD03xAXBPm/X30ksvxe//8Oc4d/GLuLm6fv8Lf7VnelecPflEvPrMockdcgSGD4Bt9Xq9eOfv/4y//e93sbyD0du0Z3p3/OOPz8TTB/ZWf7gReakTgG11u9347wNH7npZc1jLa7fi3SvXKj7VeAwfANv64cZKfPjVUoz62mC/H/HBl0vx442Vag82BsMHwLYufLw49j06EXHhk/HvUxXDB8C2Fr7rjfwy56bltfVY+Pbnik40PsMHwLZ6y2sV3We1kvtUwfABsK3u7FRF95mu5D5VMHwAbGvu0W7MTI03FbNTu2LusYcqOtH4DB8A2zp1/MDY9+hHxKlj49+nKoYPgG098uBMPPv4vuh0Rru+04l47si+pB5cbfgAGOj1E4djdmr3SNfOTu2O0ycOV3yi8Rg+AAY6enBvnD05F3umdzYZG8/qnEvqcWUREdX8uQ4AWdt80PS5iwuxvHZr4JNcOp2N0jt7ci65B1RHeEg1ADvw2eL1ePfKtfjgy6XoxMaH0zdtfh/fc0f2xekTh5MrvU2GD4Ad+/HGSlz4ZDEWvv05esur0Z2djrnHHopTx3wDOwAkxR+3AFAUwwdAUQwfAEUxfAAUxfABUBTDB0BRDB8ARTF8ABTF8AFQFMMHQFEMHwBFMXwAFMXwAVAUwwdAUQwfAEUxfAAUxfABUBTDB0BRDB8ARTF8ABTF8AFQlP8DZQ6J2Q6oMHgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "np.random.seed(0)\n",
    "nx.draw(G)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our plotted graph could clearly use some improvement. First of all, we need to make our arrow bigger. Also, we will benefit by adding labels to the nodes. \n",
    "\n",
    "**Listing 18. 14. Tweaking the graph visulization**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "labels = {i: G.nodes[i]['webpage'] for i in G.nodes}\n",
    "nx.draw(G, labels=labels, arrowsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The arrow is now bigger, and the node labels now partially visible. Unfortunately, these labels are obscured by the dark node color. However, we can make the labels more visible by changing the node color to something lighter, like cyan.\n",
    "\n",
    "**Listing 18. 15.  Altering the node color**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "nx.draw(G, labels=labels, node_color=\"cyan\", arrowsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Within our latest plot, the labels are much more clearly visible. We see the directed link from _SciPy_ to _NumPy_. Now, lets add a reverse web-link from _NumPy_ to _SciPy_ in order to stay consistent with our earlier discussion.\n",
    "\n",
    "**Listing 18. 16. Adding a back-link between webpages**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "G.add_edge(0, 1)\n",
    "nx.draw(G, labels=labels, node_color=\"cyan\", arrowsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to expand our network by adding two more webpages; _Pandas_ and _Matplotlib_. These webpages will correspond to nodes containing ids 2 and 3, respectively.\n",
    "\n",
    "**Listing 18. 17. Adding multiple nodes to a graph object** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We've added these nodes to our graph:\n",
      "[(2, {'webpage': 'Pandas'}), (3, {'webpage': 'Matplotlib'})]\n",
      "\n",
      "Our updated list of nodes is:\n",
      "[(0, {'webpage': 'NumPy'}), (1, {'webpage': 'SciPy'}), (2, {'webpage': 'Pandas'}), (3, {'webpage': 'Matplotlib'})]\n"
     ]
    }
   ],
   "source": [
    "webpages = ['Pandas', 'Matplotlib']\n",
    "new_nodes = [(i, {'webpage': webpage})\n",
    "             for i, webpage in enumerate(webpages, 2)]\n",
    "G.add_nodes_from(new_nodes)\n",
    "\n",
    "print(f\"We've added these nodes to our graph:\\n{new_nodes}\")\n",
    "print('\\nOur updated list of nodes is:')\n",
    "print(G.nodes(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've added the two more nodes. Lets visualize the updated graph.\n",
    "\n",
    "**Listing 18. 18. Plotting the updated 4-node graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "labels = {i: G.nodes[i]['webpage'] for i in G.nodes}\n",
    "nx.draw(G, labels=labels, node_color=\"cyan\", arrowsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our current web-link network is disconnected. We'll proceed to add two more web-links.\n",
    "\n",
    "**Listing 18. 19. Adding multiple edges to a graph object** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "G.add_edges_from([(0, 2), (3, 0)])\n",
    "nx.draw(G, labels=labels, node_color=\"cyan\", arrowsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can infer that _NumPy_ is our most popular site, since it has more inbound links than any other page. We've basically developed a simple metric for ranking websites on the internet. That metric equals the number of inbound edges pointing towards the site, also known as the **in-degree**. We can also compute the in-degree directly from the graph's adjacency matrix. In order to demonstrate how, we'll first print-out our updated adjacency matrix.\n",
    "\n",
    "**Listing 18. 20. Printing the updated adjacency matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 1. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "adjacency_matrix = nx.to_numpy_array(G)\n",
    "print(adjacency_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ith column in the matrix tracks the inbound edges of node `i`. The total number of inbound edges equals the number of non-zero ones within that column. Therefore, the sum of values in the column is equal to the node's in-degree. In general, executing `adjacency_matrix.sum(axis=0)` will return a vector of in-degrees. That vector's largest element will correspond to the most popular page in our Internet graph.\n",
    "\n",
    "**Listing 18. 21. Computing in-degrees using the adjacency matrix** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPy has an in-degree of 2.0\n",
      "SciPy has an in-degree of 1.0\n",
      "Pandas has an in-degree of 1.0\n",
      "Matplotlib has an in-degree of 0.0\n",
      "\n",
      "NumPy is the most popular page.\n"
     ]
    }
   ],
   "source": [
    "in_degrees = adjacency_matrix.sum(axis=0)\n",
    "for i, in_degree in enumerate(in_degrees):\n",
    "    page = G.nodes[i]['webpage']\n",
    "    print(f\"{page} has an in-degree of {in_degree}\")\n",
    "\n",
    "top_page = G.nodes[in_degrees.argmax()]['webpage']\n",
    "print(f\"\\n{top_page} is the most popular page.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we can compute all in-degrees using the NetworkX `in_degree` method.\n",
    "\n",
    "**Listing 18. 22. Computing in-degrees using NetworkX**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert G.in_degree(0) == 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tracking the mapping between node ids and page-names can be slightly inconvenient. However, we can bypass that inconvenience by assigning string ids to individual nodes.\n",
    "\n",
    "**Listing 18. 23. Using strings as node-ids within a graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "G2 = nx.DiGraph()\n",
    "G2.add_nodes_from(['NumPy', 'SciPy', 'Matplotlib', 'Pandas'])\n",
    "G2.add_edges_from([('SciPy', 'NumPy'), ('SciPy', 'NumPy'),\n",
    "                   ('NumPy', 'Pandas'), ('Matplotlib', 'NumPy')])\n",
    "assert G2.in_degree('NumPy') == 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus far, we've focused on directed graphs, in which traversal between nodes is limited. Each directed edge is like a one-way street that forbids travel in a certain direction. What if instead, we treated every edge as though it was two-way street? Our edges would thus be **undirected**, and we'd obtain an **undirected graph**. In an undirected graph, we can traverse connected nodes in either direction.\n",
    "\n",
    "## 18.2 Utilizing Undirected Graphs to Optimize the Travel-Time Between Towns\n",
    "\n",
    "Suppose that a road connects two towns, _Town 0_ and _Town 1_. The driving time between the towns is 20 minutes. Lets record this information in an undirected graph.\n",
    "\n",
    "**Listing 18. 24. Creating a 2-node undirected graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()\n",
    "G.add_edge(0, 1)\n",
    "G[0][1]['travel_time'] = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our travel-time is an attribute of the edge `(0, 1)`. Given an attribute `k` of edge `(i, j)`, we can access that attribute by running `G[i][j][k]`. Hence, we can access the travel-time by running `G[0][1]['travel_time']`.\n",
    "\n",
    "**Listing 18. 25. Checking the edge attribute of a graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It takes 20 minutes to drive from Town 0 to Town 1.\n",
      "It takes 20 minutes to drive from Town 1 to Town 0.\n"
     ]
    }
   ],
   "source": [
    "for i, j in [(0, 1), (1, 0)]:\n",
    "    travel_time = G[i][j]['travel_time']\n",
    "    print(f\"It takes {travel_time} minutes to drive from Town {i} to Town {j}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imagine an additional _Town 2_  that is connected to _Town 1_ but not _Town 0_. There is no road between _Town 0_ and _Town 2_. There is a road between  _Town 1_ and _Town 2_. The travel-time on that road is 15 minutes. Let's add this new connection to our graph. Afterwards, we'll visualize the graph using `nx.draw`.\n",
    "\n",
    "**Listing 18. 26. Visualizing a path between multiple towns**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "G.add_edge(1, 2, travel_time=15)\n",
    "nx.draw(G, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Traveling from _Town 0_ to _Town 2_ requires us to first traverse _Town 1_. Hence, the total travel-time is equal to the sum of `G[0][1]['travel_time']` and `G[1][2]['travel_time']`.\n",
    "\n",
    "**Listing 18. 27. Computing the travel-time between towns**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It takes 35 minutes to drive from Town 0 to Town 2.\n"
     ]
    }
   ],
   "source": [
    "travel_time = sum(G[i][1]['travel_time'] for i in [0, 2])\n",
    "print(f\"It takes {travel_time} minutes to drive from Town 0 to Town 2.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our computation was trivial, since there is just one route between _Town 0_ and _Town 2_. However, in real-life, many routes can exist between localized towns. Lets build a graph containing more than a dozen towns. These cities will be spread across multiple counties. Within our graph model, the travel-time between towns will increase when cities are in different counties. We'll assume that:\n",
    "\n",
    "A. Our towns cover six different counties.\n",
    "\n",
    "B. Each county contains 3 - 10 towns.\n",
    "\n",
    "C. 90% of towns within a single county are directly connected by road.\n",
    "* The average travel-time on a county road is 20 minutes.\n",
    "\n",
    "D. 5% of cities across different counties are directly connected by a road.\n",
    "*  The average travel-time across an intra-county road is 45 minutes\n",
    "\n",
    "### 18.2.1 Modeling a Complex Network of Cities and Counties\n",
    "\n",
    "Lets start by modeling a single county that contains five towns.\n",
    "\n",
    "**Listing 18. 28. Modeling five towns in the same county**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()\n",
    "G.add_nodes_from((i, {'county_id': 0}) for i in range(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll assign random roads to our five towns.\n",
    "\n",
    "**Listing 18. 29. Modeling random intra-county roads**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np \n",
    "np.random.seed(0)\n",
    "\n",
    "def add_random_edge(G, node1, node2, prob_road=0.9, \n",
    "                    mean_drive_time=20):\n",
    "    if np.random.binomial(1, prob_road):\n",
    "        drive_time = np.random.normal(mean_drive_time)\n",
    "        G.add_edge(node1, node2, travel_time=round(drive_time, 2))\n",
    "\n",
    "\n",
    "nodes = list(G.nodes())\n",
    "for node1 in nodes[:-1]:\n",
    "    for node2 in nodes[node1 + 1:]:\n",
    "        add_random_edge(G, node1, node2)\n",
    "            \n",
    "nx.draw(G, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've connected most of the towns in _County 0_. In this same manner, we can randomly generate roads and towns for a second county; _County 1_.\n",
    "\n",
    "**Listing 18. 30. Modeling a second random county**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "def random_county(county_id):\n",
    "    num_towns = np.random.randint(3, 10)\n",
    "    G = nx.Graph()\n",
    "    nodes = [(node_id, {'county_id': county_id})\n",
    "            for node_id in range(num_towns)]\n",
    "    G.add_nodes_from(nodes)\n",
    "    for node1, _ in nodes[:-1]:\n",
    "        for node2, _ in nodes[node1 + 1:]:\n",
    "            add_random_edge(G, node1, node2)\n",
    "\n",
    "    return G\n",
    "\n",
    "G2 = random_county(1)\n",
    "nx.draw(G2, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently, _County 1_ and _County 2_ are stored  in two separate graphs; `G` and `G2`. We can combine these graphs together by executing `nx.disjoint_union(G, G2)`.\n",
    "\n",
    "**Listing 18. 31. Merging two separate graphs**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "G = nx.disjoint_union(G, G2)\n",
    "nx.draw(G, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our two counties appear in the same graph. Each town in the graph is assigned a unique id. Now, it's time to generate random roads between the counties.\n",
    "\n",
    "\n",
    "**Listing 18. 32. Adding random inter-county roads**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "def add_intracounty_edges(G):\n",
    "    nodes = list(G.nodes(data=True))\n",
    "    for node1, attributes1 in nodes[:-1]:\n",
    "        county1 = attributes1['county_id']\n",
    "        for node2, attributes2 in nodes[node1:]:\n",
    "            if county1 != attributes2['county_id']:\n",
    "                add_random_edge(G, node1, node2,\n",
    "                                prob_road=0.05, mean_drive_time=45)\n",
    "    return G\n",
    "\n",
    "G = add_intracounty_edges(G)\n",
    "np.random.seed(0)\n",
    "nx.draw(G, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We’ve successfully simulated two interconnected counties. Now, we’ll simulate six interconnected counties.\n",
    "\n",
    "**Listing 18. 33. Simulating six interconnected counties**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "G = random_county(0)\n",
    "for county_id in range(1, 6):\n",
    "    G2 = random_county(county_id)\n",
    "    G = nx.disjoint_union(G, G2)\n",
    "\n",
    "G = add_intracounty_edges(G)\n",
    "np.random.seed(1)\n",
    "nx.draw(G, with_labels=True, node_color='khaki')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We’ve visualized our six-county graph. However, individual counties are tricky to decipher in the visualization. Fortunately, we can improve our plot by coloring each node based on county id. Doing so requires that we modify our input into the `node_color` parameter.\n",
    "\n",
    "**Listing 18. 34. Coloring nodes by county**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "county_colors = ['salmon', 'khaki', 'pink', 'beige', 'cyan', 'lavender']\n",
    "county_ids = [G.nodes[n]['county_id'] \n",
    "              for n in G.nodes]\n",
    "node_colors = [county_colors[id_] \n",
    "               for id_ in county_ids]\n",
    "nx.draw(G, with_labels=True, node_color=node_colors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The individual counties are now visible. Most counties form tight clumps within the network. Later, we’ll proceed to extract these clumps automatically, using network clustering. For now, however, we’ll focus our attention on computing the fastest travel-time between nodes.\n",
    "\n",
    "### 18.2.2 Computing the Fastest Travel-Time Between Nodes\n",
    "\n",
    "Suppose we want to know the fastest travel-time between _Town 0_ and _Town 30_. In the process, we’ll need to compute the fastest travel-time between _Town 0_ and every other town. Initially, all we know is the trivial travel-time between _Town 0_ and itself; 0 minutes. Let’s record this travel-time in a `fastest_times` dictionary. \n",
    "\n",
    "**Listing 18. 35. Tracking the fastest-known travel times**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "fastest_times = {0: 0}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can answer a simple question; what is the known travel-distance between _Town 0_ and its neighboring towns? In NetworkX, we can access the neighbors of _Town 0_ by executing `G.neighbors(0)`. Alternatively, we can access the neighbours simply by running `G[0]`.\n",
    "\n",
    "**Listing 18. 36 Accessing the neighbors of _Town 0_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The following towns connect directly with Town 0:\n",
      "[3, 4, 6, 7, 13]\n"
     ]
    }
   ],
   "source": [
    "neighbors = list(G.neighbors(0))\n",
    "assert list(neighbors) == list(G[0])\n",
    "print(f\"The following towns connect directly with Town 0:\\n{neighbors}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we’ll record the travel-times between _Town 0_ and each of its five neighbors. We’ll use these times to update `fastest_times`.\n",
    "\n",
    "**Listing 18. 37 Tracking the travel-times to neighboring towns** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It takes 18.04 minutes to drive from Town 0 to Town 7.\n",
      "It takes 18.4 minutes to drive from Town 0 to Town 3.\n",
      "It takes 18.52 minutes to drive from Town 0 to Town 4.\n",
      "It takes 20.26 minutes to drive from Town 0 to Town 6.\n",
      "It takes 44.75 minutes to drive from Town 0 to Town 13.\n"
     ]
    }
   ],
   "source": [
    "time_to_neighbor = {n: G[0][n]['travel_time'] for n in neighbors}\n",
    "fastest_times.update(time_to_neighbor)\n",
    "for neighbor, travel_time in sorted(time_to_neighbor.items(), \n",
    "                                    key=lambda x: x[1]):\n",
    "    print(f\"It takes {travel_time} minutes to drive from Town 0 to Town \"\n",
    "          f\"{neighbor}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes approximately 45 minutes to drive from _Town 0_ to _Town 13_. Is this the fastest travel-time between these two towns? Not necessarily! It’s possible that a detour through another town will speed-up travel. Consider, for instance, a detour through _Town 7_. It’s our most proximate town, with a drive-time of only 18 minutes. What if there’s a road between _Town 7_ and _Town 13_?  If that road exists, and its travel-time is under 27 minutes, then a faster route to _Town 13_ is possible! We can potentially shave-off minutes from travel, if we examine the neighbors of _Town 7_. Lets carry-out that examination thusly:\n",
    "\n",
    "1. First, we’ll obtain the neighbors of _Town 7_.\n",
    "\n",
    "2. Next, we’ll obtain travel-time between _Town 7_ and every neighboring _Town N_.\n",
    "\n",
    "3. We’ll add 18.4 minutes to the travel-time obtained in the previous step. This represents the travel-time between _Town 0_ and _Town N_, when we take a detour through _Town 7_.\n",
    "\n",
    "4. If _N_ is present in `fastest_times`, we’ll check if the detour is faster than `fastest_times[N]`.\n",
    "\n",
    "5. If _N_ is not present in `fastest_times`, then we will update that dictionary with the travel-time computed in Step 3.\n",
    "\n",
    "**Listing 18. 38 Searching for faster detours through _Town 7_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No detours were found.\n",
      "We've computed travel-times to 3 additional towns.\n"
     ]
    }
   ],
   "source": [
    "def examine_detour(town_id):\n",
    "    detour_found = False\n",
    "    \n",
    "    travel_time = fastest_times[town_id]\n",
    "    for n in G[town_id]:\n",
    "        detour_time = travel_time + G[town_id][n]['travel_time']\n",
    "        if n in fastest_times:\n",
    "            if detour_time < fastest_times[n]:\n",
    "                detour_found = True\n",
    "                print(f\"A detour through Town {town_id} reduces \"\n",
    "                      f\"travel-time to Town {n} from \"\n",
    "                      f\"{fastest_times[n]:.2f} to \"\n",
    "                      f\"{detour_time:.2f} minutes.\")\n",
    "                fastest_times[n] = detour_time\n",
    "        \n",
    "        else:\n",
    "            fastest_times[n] = detour_time\n",
    "    \n",
    "    return detour_found\n",
    "\n",
    "if not examine_detour(7):\n",
    "    print(\"No detours were found.\")\n",
    "    \n",
    "added_towns = len(fastest_times) - 6\n",
    "print(f\"We've computed travel-times to {added_towns} additional towns.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We’ve uncovered travel-times to three additional towns. However, we have not uncovered any faster detours for travel to neighbors of _Town 0_. Lets choose another viable detour candidate. We’ll select a town that’s proximate to _Town 0_, whose neighbors we have not examined. Doing so requires that we:\n",
    "\n",
    "1. Combine the neighbours of _Town 0_ and _Town 7_ into a pool of detour candidates.\n",
    "2. Remove _Town 0_ and _Town 7_ from the pool of candidates, leaving behind a set of unexamined towns.\n",
    "2. Select an unexamined town with the fastest known-travel distance to _Town 0_.\n",
    "\n",
    "**Listing 18. 39 Selecting an alternative detour candidate**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our next detour candidate is Town 3, which is located 18.4 minutes from Town 0.\n"
     ]
    }
   ],
   "source": [
    "candidate_pool = set(G[0]) | set(G[7])\n",
    "examined_towns = {0, 7}\n",
    "unexamined_towns = candidate_pool - examined_towns\n",
    "detour_candidate = min(unexamined_towns, \n",
    "                       key=lambda x: fastest_times[x])\n",
    "travel_time = fastest_times[detour_candidate]\n",
    "print(f\"Our next detour candidate is Town {detour_candidate}, \"\n",
    "      f\"which is located {travel_time} minutes from Town 0.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our next detour candidate is _Town 3_. We’ll proceed to check _Town 3_ for detours.\n",
    "\n",
    "**Listing 18. 40 Searching for faster detours through _Town 3_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No detours were found.\n",
      "9 detour candidates remain.\n"
     ]
    }
   ],
   "source": [
    "if not examine_detour(detour_candidate):\n",
    "    print(\"No detours were found.\")\n",
    "\n",
    "def new_neighbors(town_id):\n",
    "    return set(G[town_id]) - examined_towns\n",
    "\n",
    "def shift_to_examined(town_id):\n",
    "    unexamined_towns.remove(town_id)\n",
    "    examined_towns.add(town_id)\n",
    "\n",
    "unexamined_towns.update(new_neighbors(detour_candidate))\n",
    "shift_to_examined(detour_candidate)\n",
    "num_candidates = len(unexamined_towns)\n",
    "print(f\"{num_candidates} detour candidates remain.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, no detours were discovered. Nonetheless, nine detour candidates remain in our `unexamined_towns` set. Lets iteratively examine the remaining candidates. The code below will iteratively:\n",
    "\n",
    "1. Select an unexamined town with the fastest known travel-time to _Town 0_.\n",
    "2. Check that town for detours using `examine_detour`.\n",
    "2. Shift the town’s id from `unexamined_towns` to `examined_towns`.\n",
    "4. Repeat Step 1 if any unexamined towns remain. Terminate otherwise.\n",
    "\n",
    "**Listing 18. 41 Examining every town for faster detours**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A detour through Town 14 reduces travel-time to Town 15 from 83.25 to 82.27 minutes.\n",
      "A detour through Town 22 reduces travel-time to Town 23 from 111.21 to 102.38 minutes.\n",
      "A detour through Town 28 reduces travel-time to Town 29 from 127.60 to 108.46 minutes.\n",
      "A detour through Town 28 reduces travel-time to Town 30 from 126.46 to 109.61 minutes.\n",
      "A detour through Town 19 reduces travel-time to Town 20 from 148.03 to 131.23 minutes.\n"
     ]
    }
   ],
   "source": [
    "while unexamined_towns:\n",
    "    detour_candidate = min(unexamined_towns, \n",
    "                       key=lambda x: fastest_times[x])\n",
    "    examine_detour(detour_candidate)\n",
    "    shift_to_examined(detour_candidate)\n",
    "    unexamined_towns.update(new_neighbors(detour_candidate))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We’ve examined the travel-time to every single town, and discovered five possible detours. Two of the detours reduce travel-times to _Towns 29_ and _30_ from 2.1 hours to 1.8 hours. How many other towns are within two hours of _Town 0_? Lets find out.\n",
    "\n",
    "**Listing 18. 42 Counting all the towns within a 2-hour driving range**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29 of our 31 towns are within two hours of our brewery.\n"
     ]
    }
   ],
   "source": [
    "close_towns = {town for town, drive_time in fastest_times.items()\n",
    "               if drive_time <= 2 * 60}\n",
    "\n",
    "num_close_towns = len(close_towns)\n",
    "total_towns = len(G.nodes)\n",
    "print(f\"{num_close_towns} of our {total_towns} towns are within two \"\n",
    "      \"hours of our brewery.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All but two of our towns are within two hours of the brewery. We’ve figured this out by solving the **shortest path length problem**. The problem applies to graphs whose edges contain numeric attributes, which are called **edge weights**. Additionally, a sequence of node-transitions in the graph is called a **path**. Each path occurs over a sequence of edges. The sum of edge weights in that sequence is called the **path length**. The problem asks us to compute the shortest path-lengths between some node _N_ and every single node within the graph.  A shortest path length detection algorithm is included in NetworkX.\n",
    "\n",
    "**Listing 18. 43 Computing shortest path-lengths with NetworkX**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "shortest_lengths = nx.shortest_path_length(G, weight='travel_time', \n",
    "                                           source=0)\n",
    "for town, path_length in shortest_lengths.items():\n",
    "    assert fastest_times[town] == path_length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In many real-word circumstances, we want to know the path that minimizes the distance between nodes. Calling `nx.shortest_path_length(G, weight=’weight’, source=N)` will compute all shortest paths from node _N_ to every node in G.\n",
    "\n",
    "**Listing 18. 44 Computing shortest paths with NetworkX**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 13, 28, 30]\n"
     ]
    }
   ],
   "source": [
    "shortest_path = nx.shortest_path(G, weight='travel_time', source=0)[30]\n",
    "print(shortest_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Driving time is minimized if we travel from _Town 0_ to _Town 13_ to _Town 28_ and finally to _Town 30_. We expect that travel-time to equal `fastest_times[30]`. Lets confirm.\n",
    "\n",
    "**Listing 18. 45 Verifying the length of a shortest path**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The fastest travel time between Town 0 and Town 30 is 109.61 minutes.\n"
     ]
    }
   ],
   "source": [
    "travel_time = 0\n",
    "for i, town_a in enumerate(shortest_path[:-1]):\n",
    "    town_b = shortest_path[i + 1]\n",
    "    travel_time += G[town_a][town_b]['travel_time']\n",
    "\n",
    "print(\"The fastest travel time between Town 0 and Town 30 is \"\n",
    "      f\"{travel_time} minutes.\")\n",
    "assert travel_time == fastest_times[30]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 19 Dynamic Graph Theory Techniques for Node Ranking and Social Network Analysis\n",
    "\n",
    "## 19. 1 Uncovering Central Nodes Based on Expected Traffic within a Network\n",
    "\n",
    "We need a way of ranking the towns based on expected traffic. One naive solution is to just count the number of inbound roads into each town. The edge-count of a node within an undirected graph is simply called the node’s **degree**. We can compute the degree of any node `i` by summing over the ith column of the graph’s adjacency matrix. Or, we can measure the degree by running `len(G.nodes[i])`. Alternatively, we can utilize the NetworkX degree method by calling `G.degree(i)`.\n",
    "\n",
    "**Listing 19. 1 Computing the degree of a single node**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Town 0 is connected by 5 roads.\n"
     ]
    }
   ],
   "source": [
    "adjacency_matrix = nx.to_numpy_array(G)\n",
    "degree_town_0 = adjacency_matrix[:,0].sum()\n",
    "assert degree_town_0 == len(G[0])\n",
    "assert degree_town_0 == G.degree(0)\n",
    "print(f\"Town 0 is connected by {degree_town_0:.0f} roads.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In graph theory, any measure of a node’s importance is commonly called **node centrality**. Furthermore, ranked importance based on node’s degree is called the **degree centrality**. We’ll now select the node with the highest degree centrality in `G`.\n",
    " \n",
    "**Listing 19. 2 Selecting a central node using degree centrality** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Town 3 is our most central town. It has 9 connecting roads.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "central_town = adjacency_matrix.sum(axis=0).argmax()\n",
    "degree = G.degree(central_town)\n",
    "print(f\"Town {central_town} is our most central town. It has {degree} \"\n",
    "       \"connecting roads.\")\n",
    "node_colors[central_town] = 'k'\n",
    "nx.draw(G, with_labels=True, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Town 3_ our most central town. How does _Town 3_ compare with the second most central town? We’ll quickly check by outputting the second highest degree in `G`.\n",
    "\n",
    "**Listing 19. 3 Selecting a node with the second highest degree centrality**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Town 12 has 8 connecting roads.\n"
     ]
    }
   ],
   "source": [
    "second_town = sorted(G.nodes, key=lambda x: G.degree(x), reverse=True)[1]\n",
    "second_degree = G.degree(second_town)\n",
    "print(f\"Town {second_town} has {second_degree} connecting roads.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Town 12_ has eight connecting roads. It lags behind _Town 3_ by just one road. What would we do if these two central towns had equal degree rankings? Lets challenge ourselves to find out, by removing an edge connecting _Towns 3_ and _9_.\n",
    "\n",
    "**Listing 19. 4 Removing an edge from the most central node**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LJm2SnIYoiuTMmRMPD48Ea+19zOPHj6latSrLly/n119/BSAgIICSJUuyf/9+nJ2dDV43cOBAcuXKxfDhw5Mc4z1SdBSa2eMNvlRExKrJMn0RV3/vQsFMuhCGrjsPksPGmql1XOI2zmCHyYC/kj2ujIyMzLfMV0/3IZiYoOryG5r1y5BeBSBok7HyMzFB2bITCgddkLsgCDRs2JAGDRrwau5UCA0yeNn4k150K1OM3OmSDva+6nmG9QdPolQq43xUKlW8Y7lz52bw4MHUqlUr3jlD1wwYMID27dszadIkHB0dmThxInXq1CEyMpIzZ84YHCNz5sx4eHjQsmXLZI2hVCoRgl7rPGcNCN/9N29RKgS96AGUyJqZ075+8dqKQa85dvQoNWrWRCVniJGRkfnO+SaeYoKFJaru/dj31zCqWSixMjePn9FFpQIJhHyOKGs1RMgWf1UnCAJ2WbMiGRC+a/6vOP74KRd7d0zWnNLZ2VHcPjNarTbeR6PRoNVqUavVREdHkydPHs6fP0/+/PkNtv/4mvcfR0dHRowYQZ48eXjx4gWmpqaMGTMmwfYRERH4+/tTu3btZI/hYp+T7e2akN6Ax2hEbCzpzOLu26UzNyU8xoBTkCAwYcxoOvg8oXXr1rRr147KlSujSCTVmoyMjMy3yjchfACPfZ/SfdUG7t6+jTLoFeLlc0hhIaDVgLkFinwFUZSrjGBjm3hH6TLoyhZ9YsE9/cQP3+AQ8s9ZDkB4rBqtJHJnqTsX+nwihgoFhctXpGiNesmae1RUFNmyZWPMmDHY2dkl+55HjRrFjBkzOH36NJUrV060bXR0NBkyZODu3bv6yu1JIfr56sI6YuJXi7AyNSX0E5ELjYnF2sDeqAI4ffYsjx49ZsuWLfz2228EBwfTtm1bXF1dKVOmjBzsLiMj893w1ff43uPq6krRokUZPXr0Z/UjPn+Kdu2SeOEMkbHqOA/6OV6XeBIcysJGtclsFTflWLRWy9E8Rajn2gErK6tkjduiRQuaN29Op06dktVekiTq1avH27dvyZQpE/v27UvSjFisWDHWr19P6dKlkzdGWCiaeVN0Lw+f8H6P71rfLjja6cyd3XYeJLuhPT4LS0z+mBTn0K1bt9iyZQubNm1CEATatWtHu3btKFo0iSoSMjIyMl+Zb8JWdeXKFU6dOsXgwYM/u6+br9/yPCx+ALqlqQnZbKz0HytTE8xVyniiB3DnTTDt+w3Azs6OZs2acfr0aZJ6P2jSpAl79uxJ9jyXLVtGcHAwHh4eSJJE//79kxyjZMmSXL9+PVn93759m7+mTuPCc3+D561MTWjm5MiEk15ExKrxevqcffce0aHkJ+EMShWCAY/OYsWKMWnSJB48eMCmTZuIioqifv36FC9enClTpvDw4cNkzVNGRib1iGIsMTGviIryJTLSh8hIH6KinhIb+xZJSoGz4E/GN7Hiq1u3Ls2bN+e3335LdR+3b99m3LhxnDlzhtWD+1FLE4aQinRokRot070fU6V7L44cOcL69euJiorCysqK7t2707dvX/LmzRvvusDAQBwdHQkICMA8iSwsjx8/pkKFCpw+fRonJydCQ0OpWrUqXbp0YejQoQleN3PmTF68eMHcuXMNnvf392fTpk24u7vz6tUr2rdvT5/a1cl9xdNgFYygyCh67jnC8ce+2FlYMPmX+HF8GkA1YBQmGTImek+g83D18vJi8+bNbNu2jTx58tCuXTvatGlD7ty5k7xeRkYmeWi10ajVrxHFWMDQI1y39aBUWmJqmglB+GZ2tb4JvvqK79ixY/j4+ODm5paq6x88eEDHjh2pUaMG5cuX5+HDh9Qb9icK+/wprlGnRsC8WCly1qxDt27dyJAhA8+fP+fgwYO4uLiwYMECChYsiJOTE8uWLSM8/MPKMnPmzBQvXpz//vsv0TFEUaRbt26MHDkSJyedyNja2vK///2POXPmsGPHjgSvNbTiCw8PZ/369dStW5ciRYpw69YtZs2aha+vLzNnzsShTgNIYE8wo6UFO1ybEjxqAI+G9IwneqJCwaU3IZSpVp1Tp04lel8ACoWCqlWrsnDhQp4/f860adO4c+cOpUqVwsXFhUWLFvHy5csk+5GRkUkYjSaMmJgXiGIMhkWPd8cltNoIoqL83gmkzHu+qvCJosjIkSOZMmUKJiaJVaWLz5MnT+jevTuVK1emcOHCPHr0iOHDh2NlZYWgUKBs0xUhV15IZr9ahZIrb0MpPHwsCAJnz57l5s2b+v203bt38/btW1avXo2VlRX9+vXDzs6OunXrcuLECURRpEmTJmzevJldu3axatUq1q5dy4EDB4iMjNSPM3/+fLRaLYMGDYozfu7cudm7dy99+vTh/PnzBudYqlQprl+/jlqt5uDBg3To0IFcuXKxdetWevTowfPnz1m1apU+rAJAUChQdewFponlsjGAQoHCJh1Vps9j3LhxdOrUifbt2+vTwiWFSqXil19+YcWKFfj7+zNixAjOnj1LoUKFqFOnDitXruTt27cpm5OMzE+OVhtJbGwgCQuewauIjn6BJKUiScgPylc1dW7ZsoVZs2Zx/vz5ZLvG+/n5MWXKFLZu3Urfvn0ZMmQI6dOnN9hWErWIJw8jXjijO2Co6K2pme4hX7kGiqq1uHz5ChMnTuTy5cv88ccfZM+enWHDhlGrVi1mzZpFpky6rCaBgYH8+++/LFu2jBcvXmBmZkbGjBnx8/PD1tYWrVaLIAgoFAq0Wi3dunWjUaNGdOzYkbNnzyYY7L5v3z569+6Np6dnnGoOkiRx+fJlqlevjqWlJfnz56dTp060adOGzJkzJ/m96T08Y2PiebzGQ6mCdOlRdf0d4V0i8YiICKZOncqyZcsYMWIEAwcOxDSlYoouufeBAwfYvHkzR48epXr16rRr144mTZoYzIwjIyOjQ5JEoqKeABJLl67D3X0n3t73aN26Mf/+O1PfbseO/zFlynyePw8gV65sjB8/jMaN66BQWGBubji5x89GmgqfJIpIj+4h+jyAiHBQKhFs06MoWgpN+ox6k2Ht2rWT7CsgIIBp06bh7u6Om5sbw4cP14tQkvPQaJBuX0d79hQEB4FGDSamCBkzoahcA6FQsXjld65evcrEiRM5f/48/fv3x8/Pjx07djBz5kw6deqkd9+Pjo6mQYMGnDlzBk0iaddMTEzQaDTUrVuXgwcPJur+v2DBApYsWYKnpyfBwcFs2LABd3d3ff9//PEHvXr1Sta9x/kegoPQ/ncYyfsaCIr4ibxNzUAQEMpVRulSG8Es/l7lgwcPGDhwID4+PixYsIBffvklxfN4T2hoKHv37mXTpk2cOXOGevXq0a5dOxo0aICFhUWq+5WR+RHRaEKJjX0NSOzZcxiFQsGxYx5ERUXrhe/FiwCKFKnJli1LqVu3GocP/0fHjv25ffsUWbJkwtw8DwqFvN+XJsInRUfpck2eO61LQP3xSkuhAIWSVyhYfusB4zZuQRASXu29fv2amTNnsnLlSjp37szIkSPJmjWrsaecINeuXWPSpEl4eXnRpk0bTp06hZ2dHUuXLiVPnjxUr16dGzduEBUVlaz+LC0t6dixI0uXLk1Q/IKCgmjdujWXL19GpVLRtm1bOrdvTzlrM57v2ISdEkwFQbcys02HooILipLlDAqVIaToKMTrF5Hu3kKKjASFAsHaBkUpZ4TCxRCUif9hSJLEvn37GDRoEGXLlmX27NnkyZO8/KEJ8ebNG3bu3MnmzZu5cuUKjRs3pl27dtSpUyfFZnAZmR8NSZKIjn6GJMV12Jsw4R+ePw/QC9/Fi9do1aoXvr4X9G3s7Z3ZunUZFSqUQaVKh6lp8hYMPzJG3+OT3gSiWTQT8dRR3SrvU/OiKIJGTRZNDCOL5kO7dR2SgZXS27dvGT16NIUKFSIiIoIbN24wZ86cLyp6oNtX27FjB0eOHMHf3x9/f38sLS2pWLEi5cqVS5Hogc7U5+7uHs8zMyYmhp07d9KiRQscHBzImDEjhQoVotGvvzKvVWPKnP4f4oEdZFeiqzwhSbqVa9BrxGP/QzNrPJr925ESqDT/MYK5BcoK1VB1+R2T34Zh0nsIqg49URQtlaTogS5DTpMmTfD29qZo0aKULl2aqVOnEhNjwJScTOzs7OjZsyfHjx/nzp07ODs7M2XKFLJnz06vXr04ceKEwZJORkGSdGndomIgOiZlOWNlZL4AkqRO1h5dmTLFKVw4P//73zG0Wi379h3F1NSUYsUKAzrHGBkjr/ik4CA0y/6B6GiSvfmqMkHI44CyQ08EhYLQ0FDmzZvHvHnzaNasGWPGjMHe3t5YU/xsvL29mTRpEocOHSI0NDTJ2LuEMDMzw9fXl/v377N+/Xp27NhByZIl6dixIy1btiRdunREhIZyYUR/ymfLlGiZJT0qE8iUBVWX3xDMv5yp8PHjxwwePJjbt28zf/58GjRoYLS+fX192bp1K5s3b+bFixf6lGkVK1b8/JRpWi28egvP/CE6VpfxB0ASwcYa8mSDjOk+HJeR+UpotVHExPjz6XP10xUfwNq1Wxk+fDLR0TGYmprg7r6A+vVr6s9bWOT76TMtGU34JFFEs3C6bg/tky5/Wb2V837+qN49qHLYWuPdv9uHBiYmaEtXZN6Ne8yePZv69eszduzYZFU7+Fp06NCBTZs2pVr43mNubk6zZs2YPn16HIGXJAntDnfEu7eSl7j7PUolQvZcKLv+nqzVmzE5cOAAAwcOpGjRosyZMyeOc44xuH//vj5bTEREhD5bTKlSpVL+h+z3Enye635OqPivUqEzzTvlgwxJpMozNmoNBLyGF68gVqP7m1IowNoCcsuC/LOh1UYSExNAUsJ34oQnXboMZM+e1ZQqVZSrV2/RunVvdu1aScmSRQBZ+MCIpk7p0T2daTMBIZjXsBZvR/Xn7aj+cUUPQK0m2vMEN6/qMrisW7fumxa9qKgo9u7d+9milyNHDkqXLs22bdsoVKgQjRs35urVqwBID+4g3b8dT/RiNBp67TlMgTnLyTh1Ac5L13Pogc+HBlot0ssXiBe9PmtuqaFhw4bcunWL8uXL4+zszPjx41NkBk6KggULMmbMGLy9vdm/fz8qlYpWrVpRuHBhxo0bx507d5LX0aNnOtETxYRFD0Ar6gTo1gN49cY4N5EUGg3ceQznrsOT57qVqCjq/q60WggJ150/ex38A7/MnGS+OpGR0Yk6z73nxo07VKniTJkyxVEoFJQtWwJn55KcPPn+eSD89KIHRhQ+0fOE4XCBZGJuYcG6kcP0Qd3fMg8ePDBKZYKAgAA8PT2JiIhgypQp3Llzh7Jly5I5c2bur1se3+sS0IgSuWxtONa1Da9H9mN8zSq037afJ29DPjRSqxG9/vtsYU4NZmZm/PXXX1y5cgVvb2+KFCnCnj17jDoXQRDipEZzd3cnPDycOnXqULJkSaZNm8bjx48NX/wsAF4EJi54nyJKcO8JBKfx/khMLFy+DYFvdWOKCXxn7wX54TN4+DTp8BSZ746XL1+yfft2vQOZo6NTnD1ujUZDdHSMvhJLdHQMGo2GsmWL4+V1ievXbwNw7Zo3Xl6XKFasEAAKRcpDkH5EjGLqlELeolkw3WAyZNCZOm8HvkGSJApmysjEWlWo7mAghVXmbJj8nvxCq6lFkiTUajUxMTFER0cTHR2t/9nQsU/P37lzh7Vr136WMwfogryDg4PjJML29/dn4eSJjMxoinkyM8+UWbyO0TUq0qJIwQ8HTc1Qtuumr1n4tTh69CgDBgzAwcGBefPm4eiYdvMRRRFPT082bdrE9u3bcXBw0KdMy5kzp04szl0HUWLhzq2sObSfmz4Pca1VlzV/jtf3ExkdzbAlc9l68hhqrYaS+Qtyev6/YG4K5YunjYlRo9WJXkxMymKTFQrInRXy5jT+nGS+CJIk8fjxYzw8PPSfwMBAqlSpQtWqVXFxcaFcuXJAMFqtLlvUlCnzmDp1QZx+/vqrP6NGDWTp0nUsWrSGV6/ekClTRnr16sDAgW6Eh0dw5swtatf+lXTp0n2FO/12MIrwiT4P0G5ZY7D8DcAFP3+cMtthqlSw5dY9Bh04wcU+ncifMX2cdlqFknMuDVMkQqk9r1QqMTc3x8zMDHNz8wR/NnQsKCiIrVu3frbwAVSsWJGcOXOSI0cO/X/Li1HkffoARTJWJS/DIygwZwUX+3SicOa4+TSFEmVRNW//2XP8XGJjY5k/fz7Tp0+nd+/e/PXXX8muepFaNBoNJ06cYPPmzezevZvixYsz7feBVMxuj0KS2Hn6BApBweGL54iKiY4jfB0nj0Gj1bJg4HAy2thy7eF9yhZy0olMCUdIRiHjFPPgKfgHsnDHFoOC/MT/BQ6uTbH6yGlpRPvOjOnsBgoByhQBKzn28XtAq9Vy8+ZNvcidOXMGQRBwcXHRf4oVKxbPqiSKMURHPydlb0Yf0GhEfvttPAcPHqRr164MGDDAYN7hnwHjeD8kIHjvKZ8ru/7nzqWKsvXmXQ498KFvhU/K62g01KtXD4VCoc968unPCoUCpVIZ77/vPwqFQl+NXKVSkT59elQqlf6YiYmJ/mdDfSf2kSRJL3bJsbcnhampKc7OzoSGhuLn58ft27cJDQ3l9wK5yFcoaccQtVZLlx0H6VSqSDzRAyA0JP6xr4CpqSnDhg3D1dWVP/74gyJFijB79mxatmyZZvsNKpWKunXrUrduXZYsWcLhw4cpYpIOxbv3vBbVagFw6d4d/AI//P977+kT9np54LdtP7ZWukwyZQu9M7+Los5Uamzh04o6RxZJIkemTIzu1F0vyJ8SvP9E/PJVoqRz1imU17jzkjEK0dHRXLx4US90Z8+eJVu2bLi4uNCoUSNmzJhB3rx5k/xbUCjMUCjMEcUUeM3rEbCwyMKGDRt4+vQpCxYsoGzZstSuXZshQ4ZQsWLFVN/f94hxhM80eYVR3yMIgsE9H4WJCQ8fPkQUxXgfSZIMHk/ok5L2qWl74sQJnj9//llfm52dHTExMdja2mJjY0P27NkRRRF7m6T/WURRouvOQ5gqFcxrWMtgGykl3qBfgJw5c7JhwwZOnTpFv379WLZsGfPnz0/zfV0zMzOa1K4DV+4kubd3/o439lmzMW71v6w/coDsdpkY37UXLau/+46DQo0/wcAg/Y8JCXKSvHoD+XODSpl0W5k0JTg4GC8vL/1q7urVqzg5OeHi4kKvXr1Yu3YtWbJkSVXfZmbZiI5+/i6QPbniJ6BS2WJiojNv5smTh7///puxY8eyatUqXF1dyZ49O0OGDKFZs2ZJ1gX9ETDKHQoZ7BLc3wuOiubC8wCq2edCpVCw1fseHr5+zKpfI34/6dJ/N+Vr7Ozs6NWrF2FhqXN4MDU1pVy5cmzZsoX69evj5uZGrVq1UCgUaE4cRPI4luC1kiTRa+8RXkVEsLdDc0yUhh92oWoN6bVafcLqb4Xq1atz5coVFi9eTLVq1ejatStjx47FxiYNTIjvUWveV2pJFL/AV9zyeUTLarV4seMgZ71v8OvIwRTJ64CTvQOSJHL10iXMLCzimcLNzc1T99DwT76zjX27JggI1ClXnr/7DCTT+zy1ggBBIZAl6fJRMsblxYsXepHz8PDg0aNHODs74+LiwtixY6lUqZLR8tAKggJz85zExPgjijGIojYJRzsBlSo9JiYZ4p2xsbFh4MCB9OvXj927d/PPP/8wfPhwBg4cSPfu3bG1/cIhPF8QowmfkCU70otn8c6pRZFxJzy59zoIpaCgUKYMbG/XlEKZPvkDNTFFUbGaMabzRWjRokWq6wcqlUrKli3L3r17efv2LRs2bGDYsGGEhITQvXt3eterTQZTU4g1XEqk3/7j3A18w6HOrbBIIJ1XtCgxd99BFoyYQOXKlalWrRrVqlWjXLlyqUoubWxMTEwYOHAg7dq1Y8SIETg5OTFz5kxcXV3T0N066X4tzMwwUakY3ak7KpWK6qXKUrN0WY5cPKcTPlHi99/7ERYRrt8z/vgjCILBPeNPPx+fm9GyI5mtE3/IZEqXnotL11KqQEHehIbQd+5MOkwZw+G/3zk4iJIuPaBMmiJJEvfv39eLnIeHB8HBwXonlA4dOlCmTJk0/RsTBAVmZjnw8DiGWh1MpUplMPT/tkpli0qVDoUi8ZR/SqWSli1b0rJlS86dO8ecOXOYNGkS3bp1Y8CAAZ+djvBbxGhrWkWVWmj3bI4X0pDZypKzvTok3YEkoShR1ljTSXNMTU3ZvXs3DRo0SHGsmq2tLZs2bQIgQ4YM9OvXj759+3LlyhVWrFhB4fqNuP1bR+xM4/8P6xscyvLLNzBTKsk9a5n++KLGv9D+o3p65qamTNy5j/7BIZw5c4bTp0/Tr18/Hjx4QLly5fRCWLFixTR3NEmMrFmzsmbNGry8vPTmz4ULF1K8eHHjDmSiSpbbf4l8icePqjUalCYqqlWrRokSJShRogTFixfXvx3r3MzjC+LHzlWffsyTsVVgbWlJucK6AOSsGe1YOHA42Vs2IDQi/N1eZCLhDzKpRqPRcP369TiOKObm5ri4uFC1alWGDx+Ok5OTUcKbUoIgCIwbN5VevXphYWGPVhsNiO/OKVEoLBLNgZwQFStWZMuWLTx58oQFCxZQqlQp6taty5AhQyhfvryR7+LrYbzMLVotmrmTITwVeyAqE4RSzqh+bWmMqXxR9u7di6ura5yaewmhVCpJnz49J0+eTPTBHhkZyc2VSygS+Azz1JgpFQqE0uVRNWod71RISAheXl6cPn2a06dPc+3aNYoXL64XwipVqpAhQ3yzyJdAq9Xy77//Mm7cONq3b8/48eMTLDmVYiRJF/St1pnkNRoNGq2WCWuX4xf4iuXDRqFSKpEAp86t6VL/V/5s35Xzd7yp/8cALi5dS2H7vMTaWHA27DXXr1/nxo0b3LhxA29vb7JmzaoXwhIlSlCyZEny5cuXPDPzxVsQGXc/b/SKJfgFvozjbfoxL4PekK1FfYL3nySdtbXO47RAHsguJyD+HKKiojh//rxe6M6dO0eePHn0KzoXF5dvYgV07do1GjVqhI+PT5omcQ8NDWXlypXMmzePXLlyMWTIEJo2bfrNbZ+kFOPm6gwMQLNifsoC2ZUqhKzZUXbv98VTbBmLixcvMmDAAK5du4ZWq0X9icnJ3FxXNaF+/frMnz8/WfuYUkw0msV/I4WFIKT0n8jMHFWfoQjpk97viYyM5MKFC3ohPH/+PPny5dMLoYuLC9myZUvZ+J/J69ev+euvv9i3bx/Tp0+nU6dOxnmjfuoPvi9AlBi/+l8mrF0e5/S4Lj0Z360X3j6PcPt7CjceP8A+a3amuP1Gc5eaOnEp7gjp4+5FarVaHj16xI0bN+IIYmBgIEWLFo0jiCVKlIj/YvHoGTx/BZKUoCBfvn+X9NbWOObKw9uwUH6fO4NXb99ycu5SAGLUsbjfvUr1+vW+6axH3xpBQUF4enrqV3PXr1+nePHiepGrUqUKdnZ2X3ua8ejatSuFChXizz///CLjaTQadu3axezZswkMDGTgwIF069Ytbffl0xCjlyWS/P3QrFuq258Sk8hyb2KKkD0nyvZuyS6p8y1z//595s+fz/79+wkNDUWpVJIhQwY6d+5Mr169UuzJJb19g2b5XF3SbymZmUZMTFF27oMiV+oSe6vVaq5cuaIXQk9PTzJlyqQXwmrVqmFvb/9F0h5duHCBfv36oVKpWLRoEaVLl076osRQq+HcjdSbBM1MoULyA9hDQkK4detWHEG8efMmGTJkiCOEZYsWo8DbGAQpYUEulMeev5Yv5lVwELaWVtQpV4GZvfuTzU63wgvWqhm5dS179uwhU6ZMNGvWjGbNmlGmTBk5RdVHPHv2LI7Z0tfXlwoVKuiFrnz58l/V9J8cAgICcHJy4uHDh19FlM+ePcs///zDiRMn6NGjB/3790+1U6IkadFowhDFGCRJRBAUCIIpKpVNmtYNTJt6fKEhaD1PIF17VxMqjpOGACYmYGWtq3pepmK8IrAyH5BC3upeJMLDEl1JSyamCCamqDr3RshqvCrLoihy69YtvRCePn0aU1NTXFxc9EJYuHDhNHu4iqLIqlWrGDVqFC1btmTy5MlkzPgZnotP/cHXP2Upy0AXJF7M8bOTVYuiyJMnT+KtDlf0/4PqJVMp7AoFFHaAzBkQRZHz58+za9cudu3aRUxMjF4Eq1Wrlnau6qIIb0N1ade0oi6swtpS9/lKwitJEnfu3InjcRkREaEXuapVq1KqVKnvrt7j+PHjCQgIYOnSpV91Hj4+PsyfP5+1a9dSv359hgwZ8i7DTNKIYgxq9Vu02vdbRJ/KkIBCYY6JSQaUSuMnZkjbCuxqNZL3NcSHdyEyApRKSJceRYmyCLkd5DfRZCJJItKj+4ieJ5H8nugK0L5Dq47laUQ0k497oChcnK49elC9evU0+24lSeLhw4dxhDA8PDyOEJYsWdLoewBBQUGMGTOG7du3M3nyZHr06JE686ck6UyL/q+TLX5aJJSF80HWtHm7liSJzctX0dS+EJbmKbR8CIClBZQtEk9g3j/4d+3axe7du/Hx8eHXX3+lWbNm1KtXD0tLy8+ffEysroLEi0DddytJumfY+7mYmUDu7JAlg+7vPw15b614L3JnzpzB1tZWL3IuLi4UKlTou37uREdHkzdvXk6ePPnN5DUOCQlhxYoVzJs3j7x58zJkyBAaN26c4DNArQ5DrQ4keXGIAipVBkxM0hv13y1NhU/G+EihwUhvAnXZckxMdaEkGTPx5s0b3N3dWb58OTExMfTo0YMuXbqQPXv2pDv9TN6bj94L4YsXL6hUqVKcEAozs5QlOUiIq1ev0q9fP9RqNQsXLky9p9mzAHjyQvdzAgIYHh2FoFDQd+FsFrivTZP9jMjISPr06cO1a9c4tH4TOUKjk22KVWs1RGk0XJIiKVKyBFmzZk304fDs2TP27NnD7t27uXDhArVq1aJZs2Y0btw4dSazV0Fwz0f3/ErsMaJQ6ESvVCGwNN6WRkREBOfOndObLi9cuEC+fPniOKLkzPlj5TBdvXo1W7du5eDBg197KvHQaDTs2LGD2bNnExQUxKBBg+jatWucGMaUid57dLGIpqbGi1GVhe8HQ5IkLly4wIoVK9i+fTvVqlXDzc2NBg0afLGMDIGBgfoQitOnT3Pv3j19QG+1atWoVKnSZ+2jiKKIu7s7I0eO5Ndff2Xq1Klkzpw55R1ptfDyDWofP8SomA/iLElgY8m5F770HfMXJUuVQpIkVq9eneo5G+LBgwe0bNmSUqVKsXTpUt0KLCgEbj/SPRcSEGQJneN6UHQkc47v59ylS1y/fh2lUhnPs9TJyUnvXPUxQUFB/O9//2P37t0cO3aMMmXK0Lx5c5o2bZq8ws8Br+GBb8r2S5VKKOOUavF7/fp1nPg5b29vSpUqpRe5ypUrfzWP5C+BJEmULFmSv//+m3r16n3t6SSIJEl4eXnxzz//cOrUKdzc3OjXrx85cmQhOtqPmJhoBg0ax8mTXrx9G0K+fHkYP34Y9epVB+DkSS+GDBnPs2cvcHYuybJlM8mTJxdmZtlQKo1gpUAWvh+asLAwtm7dysqVK/H19aVr1650796d/Pnzf9F5hIaGxgmhuHr1qt5zrlq1alStWjVVD6yQkBDGjx/Phg0bGD9+PL17906VifXAgQOsXLqMHZu36Ex0JipQKZEkCWdnZwYOHMjkyZOZMGEC7dq1S3H/hti1axe9e/dm0qRJ9OrVK+5KTaMTZPwCIFZDeGQEZmZmmKhMdGKYwVZXjDadtd6kKEkS/v7+8fYOHz58SL58+eJ5lubKlUs/ZmRkJMeOHWP37t3s27eP3Llz06xZM5o3b06xYsXiryJDwuHGvdQ5CZmodBUukkitJkkSvr6+cSoWvLckvBc6Z2dnLCx+nsTcJ06coF+/fnh7e3835tpHjx4xf/581q9fz6ZNS6latQyRkVHMnbucjh1bkjt3Dg4f/o+uXQdz4cL/sLKypHjxWixaNJWGDWszceIcvLwu8t9/O1AozDE3N84KXha+nwRvb29WrlzJ+vXrKV68OG5ubrRo0cLgaiCtiYqKihNCce7cOfLly6cXQhcXlxSZaG/evEn//v0JCQlh0aJFVK5cOUXzmTFjBq9evWL27Nnxzh08eJBhw4axevVqfv31Vy5evPhZGe01Gg1//fUXW7duZdu2bTg7OyfcWJIgIorhAwbRo1s3ChctonMWMZDYICFiYmK4e/duPEGMjY2NJ4bFihXD1NQUT09P/b6gUqmkefPmNGvWjEqVKuleLK7dhZDwBEs7nfO+yZhVS7l8/y5KhYIapcoyf8Awsttl0pk98+WEnFnjzFMURby9veM4oqjV6jiOKCVKlPgp8kgmRJMmTWjUqBG9evX62lNJMcHBbxGEV5iYGP73K1/+V/76qz9BQcG4u+/gxIltAERERJInjzNeXnspVKgA5ua5k8xEkxxk4fvJiImJYe/evaxYsYLLly/Tvn17evToQcmSJb/anNRqNVevXtUL4ZkzZ/QhFO/FMKns9ZIksXnzZoYPH07t2rWZMWNGsuMPO3bsyC+//ELXrl0N9lulShX69u2Lv78/u3bt4tSpU6l6AAcEBNC2bVssLCzYsGFDsvfVihYtypYtWyhWrFiKx0yIly9fcvPmzThieO/ePXLnzh0nI42JiQnnz59nz549BAQE0M21PVOatUcpCAmWdjp43pPwqCjqOVdEpVTRb95MXrwO5ND79GpmpsSWLsSly5f1Iufp6YmdnV0cR5QCBQp8NyubtObBgwdUqVIFX1/f73KVq9GEEhv7GkN7ey9fvsbJqRpnz+5j+fKNqNVq5s2bqD9frlwDRo8eSLNm9d/t9X2+k5ksfD8xT548YfXq1axevZqsWbPi5uaGq6vrV09O+/7t/2PPUZVKFUcInZycDD4Uw8LCmDRpEqtXr2bUqFH6OMDEKFmyJKtWraJsWcMp806cOEHv3r3x9vbm119/pUqVKowfPz5F9+Th4YGrqys9e/Zk9OjRKTLJ5sqVi3PnzpErV64UjZlS1Go19+/fj7c6DAsLo3jx4uTNm5fWZSvRoHgZTD8KAUgqy8yV+3epPrA3YQdPARAZE0PzMcMJVEfrha5q1apfxBHre6V///7Y2toyZcqUrz2VVBEb+xqNJn6ZNLVaTbNmPciXLw8LFkzmt99GkilTRiZN+kPfpnbtNnTt2pZOnVqiUFhgbv754Vqy8Mmg1Wo5evQoK1as4NixYzRv3hw3NzcqV678Tbxxvw+h+NhzNCwsTG8Gex9C8bHA3b17l/79+xMQEMDChQupXr26wb7VajW2trYEBQUl+iZds2ZNOnXqRIMGDShTpgxbt27FxcUlWXOfM2cOM2fOZM2aNdSvXz/F929tbU1AQIDRMvynlDdv3uhXh41zFiBf5rhmyqSEb+62jWw+cZRzS3TOQVpJIjZnZiwc86bxzH8MgoODyZcvHzdv3vxuvVRjYl6h1catZCOKIt26DSY0NJytW5diYmLCsGGT0GjUzJ37YcXn7NyQUaMG0KxZfRQKM8zNP/8F8Oc1mMvoUSqV1K9fn/r16/Pq1SvWrVuHm5sbkiTh5uZG586dU10/zBgIgoCjoyOOjo50794dAD8/P70QrlixAj8/P30ViveOD0eOHGHnzp107tyZKlWq8Pfff8d7cNy7d488efIkaT6aNGkSHTt2pGPHjixfvpyOHTty7dq1RJ1yQkND6d69O76+vpw/fz553pKfoFariYmJ+arZROzs7KhRowY1atSACzchKvkpCW88esDEdSvZM2WW/phSELBQfV9B41+TFStW0LBhw+9W9CRJIiQkjI/f2yRJ4rff/uTVq9fs3LlSn0SgSBFHNmzYqW8XERGJj89TnJwc3x0xTjLwL5tSXOabJ0uWLAwbNozbt2+zcuVKvL29KViwIK1ateLgwYNotUmkoftC5MqVC1dXV5YsWYK3tzePHj2id+/eBAYGMmjQIOzs7KhZsybXr19n4cKF5MqVS+8KHvtRJqGbN28mqxJE1apVKVy4MCtXrqRRo0Y0adKEPn36GCyoDDpnImdnZzJnzsyZM2dSJXqg81xNly7dN7HyBnTOKcnkod8zGowYyLz+Q3Ep8SErjVYU8fDyYv/+/Tx48CBebluZD2g0GhYsWMCgQYO+9lSSjb+/P3v37mXMmDHUr1+fzJkzM3XqDKKjP7wwDRw4lnv3HrJt279YWHxwsGvcuA63b99n9+5DREfHMG3aQooVK0ShQjpPdIXCOPHAsqlTJklCQ0PZvHkzK1aswN/fn+7du9OtW7fP8m5Ma96HULxfFV65coUCBQoQFhZGbGws8+bNo2XLlvz111+YmZkxbty4JPu8cOECLVq04OHDh0iSRPny5RkyZAjdunWL027jxo0MHDiQ2bNn07lz58+6j4cPH1K/fn0ePnz4Wf2kFkmS8Pb2ZuvWrRw5coTRzdvRqGLVOG0MmTp9A/ypPrA3I9t3oU/TuFVXYrVatlw5y8bjh7l//z7Pnz/H3t6eggULxvvkyJHj2xH9r8D27duZN28eHh4eX3sqBgkODubSpUtcvHhR/4mIiMDZ2TnOJ3v2bERFPQEknj59jpNTdczMTONsT8yfP4l27Zpy4oQnQ4dO4OnT5/o4Pnv7XIAge3XKfB2uX7/OypUr2bhxI2XKlMHNzY2mTZsaLTNLWvFxCMXOnTu5fv06NjY22Nra0qZNG4YNG5Ys54qmTZtSq1YtBg4cyK1bt6hZsyaenp4ULFiQ2NhYhg4dyqFDh9ixYwclSpT47HlfunSJPn36cOnSpc/uKzmEh4fj4eHBjh07OH36ND4+Pmi1WtKlS0fx4sXp69qR1kXLoJASLu308m0Q1Qb2ok+Tlgxv1yn+IAoBKpXSx/LFxMTw6NEj7t+/H+8THh5uUBALFixovJJVXxlJktBqIxHFKCRJCwgIggqVyhoXl5oMGTKEli2/fsm2qKgorl69Gkfknj9/TunSpfUCV758efLlyxfvZSU4OJibN89QooRjgiENSSHH8cl8daKjo9m1axcrVqzg5s2bdOzYkR49elC0aNGvPbVkERoaytChQ1m5ciUODg68ffsWOzu7OOWYHBzi55O9fv26fgVmZWXF4sWLWblyJVu3bqVDhw5kz56dNWvWkC5dOqPM89ixY0ybNo3jx48bpb+PkSSJx48fc/z4cfbs2cOlS5d4/fo1oCsQ7OzsTIsWLWjcuPGHxOAf1TVMqJKEIAiMX/MvVuZx903DD53W/ZAtExTKm6w5hoSEGBTE+/fvY2lpaVAQ8+fP/1XiU1OKJGlRq0PeeTtKfOrqL4oSN2/epWzZapiY2HzRla9Go+HWrVtxRO7evXs4OTnFETknJ6dEvabVajXLli1j0qRJ9OzZjT//7JnKnOWCnLlF5tvi0aNHrFq1itWrV2Nvb4+bmxtt27b9al6IySU0NJTs2bNTp04dbt26xZAhQ5AkSW8eVSgU8UIoFAoFbdq0oVy5cvzxxx9IkkTlypW5efMm48aNY9iwYUZ9QO3YsYONGzeyY8eOz+4rKiqKS5cucfjwYY4cOcKtW7fQaDSIooiDgwPVq1enZcuWVKtWLVFnmuCbdzELeINFMirHx0MhQJkiYPV5sWiSJBEQEMD9+/e5d+9eHEF88uQJOXLkMCiKuXPn/iaKqIpiLNHRL9Aln0vqESygVFpiapp4LtbUz0Xk4cOHcUTu+vXr5M6dO47IlSxZMtkvFJIk8b///Y9hw4aRO3duZs+eTYkSJT4jV2cGTE2Nl45OFj4Zo6HRaDh06BArVqzg1KlTtGrVih49elChQoVvcp/Gy8uLQYMGceHCBQ4dOkT//v1xcnJi7ty5ODg48OjRI06fPq0XwpCQEFxcXHB0dGTFihXcv3+fnes3EPTgMVnSZaBunTrkcsgLGdOBrZVRyvGsXLkSLy8vVq5cmaLrJEni2bNneHp6cuTIEf777z+ePXuGiYkJkiRRtGhR6tatS5MmTShbtiympqbJ6vfgwYO49eiB55I12GewS1GRZEkhIOTNqUu3loZoNBqePHliUBRfv35N/vz5KVSoUDxRzJQp0xf5/1QU1URH+6ETveQioFBYYGaW7bPmKEkSz58/jyNyly5dwtbWNo7IlS1bNtXxvNevX2fo0KE8f/6c2bNn06BBgzhzlqszyPyw+Pv7s3btWlauXImZmRlubm507NiRTJkyfe2p6Vm6dCkXL17Ui0pMTAz//PMPs2bNol+/fowcOTJOmMPz58/1eSMjn/gxoHkbCuWxx8zEFOU7b0cJEBQKXVqx3FkhayZQpt55evbs2bx48cJgOrWPiYmJ4cqVK3h5eXH48GEuXLhATEwMgiCgVCpxdnamUaNG1K5dm2LFiqV41aPRaBgzZgzu7u5s2LCBalWqwM0HEBaRrJydMRo1uy+fo83wQV/1JSgiIoKHDx/GE8V79+4BULBgwXii6OjoaLRwEkmSiI72RZK0LF26Dnf3nXh736N168b8++9Mfbs1a7Ywe/YyXr58TaVKZVm6dDrZs2dLcZWCoKCgOCJ34cIFNBpNHJErV64cWbNmTbqzJPD392fMmDHs37+fsWPH0rNnzwRrHerq8QWj1Ua8O2KoHp8FJibpv796fDIykiTpY+327dtH/fr1cXNzo1atWqmrp2dE+vbti6OjYzxX8adPnzJs2DAuXrzI3LlzadKkyYeHtVZL6NmrKCOi4u1hfYokCAgWZlCyUIrya37MmDFjMDU1ZcyYMXGOv3jxgrNnz3LmzBmOHz/O3bt3sbS0JCYmBltbW6pWrUrDhg1xqlkTlYMDUYKALZAfSOl7vJ+fH66urlhaWrJ+/foPMZ2SpCvs6/dS97PWwApGoQBzU2JzZqF6y6bUr18/WR60XxpJknjz5k2c1eF7YXxf6fy9EH4sjHnz5k1RIVuNJoLY2JeAxJ49h1EoFBw75kFUVLRe+Dw8ztOxY38OHnSnQIG8DB8+mbt3H3D48CZAwMLCcC3TiIgIrly5EkfkAgMDKVOmjF7knJ2dsbe3N+rLR2RkJP/88w9z586lR48e/PXXX8ne4/6hKrDLyBgiODiYjRs3snz5coKDg/VhEWmdiishqlWrxrhx46hdu7bB88ePH6d///7Y29szf/58HPPnJ/DoGWwEJebJ9GJVazSEx8ZwVh1ChSpVUlz3rn///uTPn5+qVavi5eWlL/cUGhqKtbU1oaGh5MiRg9q1a1O7dm1cXFzIljMnh4AZwAXADF29WgmIBVoCQ4Hk1Hs/dOgQXbt2ZcCAAYwcOdLwy4okwZtgeP4KomN1FSSUCrCxglxZdf9Flx+0fPnyzJo1i9atW6foe/iaiKLIs2fPDIriixcv4oRifCyK2bNnjycw0dF+iGLcBAATJvzD8+cBeuH7889pREdHM2fOBAD8/V9SoEAVbt48Tr58eTE1zYwomnHz5s04Ivfo0SOKFSumFzhnZ2cKFSqUZnuaoiiyYcMGRo0aRaVKlZg+fToODg5pMpaxkTO3yHwx0qdPz++//87vv//OlStXWLFiBSVKlKBSpUr06NGDxo0bp+jt+XOQJCnJ4PXatWtz7do15s+fT8WKFVnxx2jqlynPiv17DFYluP3kMZ2njufRCz8AyhYszPwBwyiYx57cr1/h4OCAvb19HM/RHDni5x189eoVZ8+e5ezZs2zZsoW3b9+SPn16lEolwcHBFCpUiA4dOlC9enWqfCKmt4AKQCjwPkHUp3lWNgO7gLLAXiC9gXvXaDSMHTuWdevWsXXrVqpVq5bwlykIkCmD7pMIWbNmZc+ePdSpU4d8+fIlmBv1W0OhUGBvb4+9vT116tSJcy46OprHjx/rBfHChQusX7+e+/fvExkZiaOjo14IS5cuQZ06pVAoEl9tSZIUJzHC+59v375Pvnz23Lp1nipVmuLg4KAXud9++43ixYt/sbCi06dPM2TIEJRKJZs3b05xRZSvjbzik/mqREZGsn37dlauXMm9e/fo3LkzPXr0oFChQmk6rp+fH2XLluXly5dJtn306BFd2nfg2OR/MDc1TbAqQXBYGMHhYdhny44oiizavY0V/9vDjVWbQCGgKVGQq/fv6p1lPDw8SJ8+PcWKFSNdunSEhYVx9epVAgMDyZQpE7Gxsbx69YpChQrRqlUrqlWrRsWKFRP0lj0P/AJEkDy3AVMgJ3AR+Hgd+vz5c9q1axfftGkkdu7cycCBAzl//rxB4f9RCA4O5sGDB3pRNDWVcHNrhY1N3P3CT1d8J0960aXLQP73v/UUKJCXP/6YzOrVW1i16h/atGmMRiOiUGT/Kl7TDx8+ZMSIEVy6dInp06fTtm3br75lkRrkFZ/MV8XS0pLOnTvTuXNn7t27x6pVq6hevToFCxakR48etG7dWleZ3BhERkNkFGi0vLp9jxZ16+vMdInsd+zbtw83Nzd2z1+CmbkZiBItqtUC4NK9O/gFRuvbprexIb2NDaB7S1cqFDx8/kx3UpRQ+es8CgMDA3n79i1hYWGcPXuW169fI0kSERERSJJEtmzZKF26NK1atWLp0qVMnTo18RUX8ASoB4Sn4OuIBZ6jE8vz6ITwvWmzf//+/Pnnn2nyUGvRogV37tyhWbNmnDp16rsss5Mc0qdPrzc5Amg04cTGviKp15KaNSszatQAOnToS0hIGP36dcPGxoqcOXXesCqVAkvLLyt6b9++ZfLkyaxdu5ahQ4fi7u7+Xf+7ySs+mW8OtVrN//73P1asWIGXlxdt27bFzc2NMmXKpHxTXhR1+09PA3SiJwggQUxsLCBhZm2lc6/Pagcf7YW8N/W5u7uzdetWKormoNbE6TqhqgTpf61JeFQUoiQysVtvRnfuAUB0bCy52zbGLktmTExM9KvN6tWr6ytNWFlZ4enpqV8VPnnyBBcXFxo3bky1atUoVaqUwYDhTsAmQBsTA7//DseOQVAQFCgAU6dCgwZw7hyMGQOXL+vutUYNmD8f6+zZWaLVcmfsWNauXcuGDRsSrGZhLCRJomPHjoiiyMaNG7/JcBdjo9VGEBOjc2z5mE9XfJ/y4IEPlSs34f79M2TIkA4QsLTMl/YTRve3uHTpUiZNmkTz5s2ZOHGiUTxAvzbyik/mm8PExIRmzZrRrFkz/Pz8WLNmDa1bt8bW1hY3Nzc6dOiQaFUEPVExcP0eaDQfeRzqHjpm78UjOhYe+cFjPyjuCOlsePXqFa6urigUCi5fvkxmOzvwuJLs+Qf/7yQRUVGsPbwf+6wf0qCpNRpKFC5MLscC+qB4R0fHeA/9ggUL6vN/5syZk5YtW3Lnzh1Wr16Nr68vlSpV0u8TOjs7E21uznZAC7p7zZ0bTp2CPHngwAFo0wZu3oS3b6FXL6hXD1Qq6NcPunUj/NAh+vj4UPniRa5cufJFKnEIgsCKFSuoUaMGU6ZMYfTo0Wk+5tdGEOLuX2s0GjQaLVqt7hMdHYNKpUSj0fLokS9Fijji5+dP//6j+P33Lu9EDwQh7R/bkiSxb98+hg8fTt68eTlx4oRRCyF/beQVn8x3gSiKnDx5khUrVnDw4EEaNWpEjx49qF69umFzXGQ0XL0DmhRUk1Ao8BZiqO/ahq5duzJ+/HidR1ysGs7d0JlFPyKpOnSiKJK5WV3urN1KlgwZEQUBRalCYJt8M5WtrS1+fn76YOI3b97oPTs9PDy4ffs2WadO5WmfPmgSCkIvUQLGjYNP8z1euQLVq0NYGCZqNReUSkp94f0af39/KlSowJw5c76JfJRpTVTUMyRJVx1kypR5TJ26IM75v/7qT9++3ahb1xUfn6dYW1vRqVNLxo0b8s47U8DUNBMqVdoVi7527RpDhgzh5cuXzJ49O1U1JL91ZOGT+e548+YNGzZsYPny5URFRdGjRw+6du36Icm0RgMXvXWClULCo6K4JEZQo+FHf+xaLZy5Gq9tUsKn0WiwaVgDr0UrKe1YSOfiX9op2em6NBoN5ubmxMbGJrjXFhYWRlW1mhsZEwhqfvkS7O3h2jUoXDjuublzYfNmOHcOU2AaMCRZMzMuV65coV69ehw5coTSpZMTZPH9otGEERub0pRdHyNgYZEXQTD+C8qLFy8YPXo0Bw4cYPz48bi5uSWah/N75vtzx5H56bGzs2PAgAHcuHGDjRs34uPjQ5EiRWjatCn79u1D+/wVaLQs3LmVcr06Y1anMl2njTfY14Q1yxFqOHPs0nkArCwsqJG3oP68JElcvX6daM0HEdVoNETHxKAVtWhFkeiYGDQaDUcvnefqg3totVpCI8IZsnguGWxscMqTFwBRK4JZ8sM1QkNDsbW1TdTBxMbGBjEh0VOroUMH6NIlvujduAETJ8LffwM6R5c3yZ6ZcSlTpgxLly6ladOm+Pv7f6VZfBmUSmt0UZWpQUClsjW66EVERDBx4kSKFy9OlixZuHfvHn369PlhRQ9k4ZP5jhEEgfLly/Pvv//y7NkzmjVrxowZMwi8chNEkRyZMjG6U3e6N2hi8PpHz/3Yfuo42e0+pFETAOn1W/bu3EXbtm3JmDEjNWvVYtnenUS/K2A7ef0qLOpVZfrGtbgfPYhFvapMXr+K4PAwXCeOIt2vNcnfvjkPnz/j0Mz5mJuZIUoSx69eJDw62uBcDBEcHJysDBgGw5NFETp1AlNTWLgw7rmHD3XOLvPmgYuL7pgkceX8efbv34+3tzcRERHx+0xDWrZsSc+ePWnevDnRKfiOvjcEQcDcPAexKbZGCCgUZpiYpCwBQmKIosi6desoXLgwt2/f1ocoGKuyyLeMbOqU+bF4G4r2xv04YpCQSbLBHwPo36Itv8+ZwYrho/ilXAUAIqKjmLhuJYv2bKdKlSo0bNiQ2lVdKBohpSgpcxwUCqbs38ajwJesWrUqWZdcvXqV7t27c/VqfDPrx9QHDn98QJKge3d48kTn3PKx27mvr25fb+RI6NNHf1ilVlNpxw6s1q7Fx8cHX19fbG1tcXBwIF++fDg4OMT55M6d2+jJBiRJon379igUCtzd3X9YT8+///6bs2dPs3793GTmMRdQKMzfJag2zlrl1KlTDBkyBFNTU/755x8qVapklH6/F37ctazMz0lIuOEV0Cds++8YpiYmNKxYJd45K3MLxvQbyHT31XEfvjcfwNvQeE4uSSEBgrkpA0f/RZmyZdmyZQtt27ZN8rrg4OBkFVvtCnjxIVMLv/0Gd+7oQho+Fr3nz6FWLejbN47oAYiSRHtra7ru2oW5uTmiKBIQEMDjx4/x8fHBx8cHT09P3N3d8fHxISAggBw5csQTxPdCmTVrykvoCIKgj+OcNm0af/31V4qu/x5YtmwZS5Ys4fTp01hYZEOjCUajCX13Nn6iZkFQYmKSAaXSOPX4Hjx4wIgRI7hy5QozZsygTZs2P+wLRmLIwifzY6FO2oQUHhnJX8sXc2TWggTbWJuaxQ9sd3KAy7d1IRDJRBRFwqIi0RTIiZ2NDRs3bqRhw4ZUrFgRe3v7RK9NrvC1AHq//8XXF5YtAzMzyPZR+Z9ly3QmzsePYcIE3ec9YWE4BQayfe5c/urcmZYtW9KxY0d9SrWqVavGGzM2NpanT5/qRdHHx4d9+/bphTIiIoK8efPGE8T3PydkTrOwsGD37t1UqFABJycnmjdvnuT9fy9s2LCBSZMmcerUKX1+WlPTTJiYZESrDUer/bgCuxKVyhaFwswowhQUFMSkSZNYv349w4cPZ+PGjd9Fsd60QhY+mR+LZLjjj1uzjE51G+CQPWfK+lGpdF6Z1+7qxC+JlZ9aqyUyNoY118/z7/C+HD9+nHLlyjFs2DA6dOjAf//9l6gDQXKFzxSd8M0HYuztE5+XgcoIVsDcnDn55dgx/Pz82LhxI/369SMsLIwOHTrQqVMnCn/iHGNqakqBAgUoUKCAwWHCwsJ48uSJXhQfP37MqVOn9L+bmpoaFMT3+Ux37dpFgwYNcHBwoFSpUkl+B986e/bsYejQoRw/fpz8+fPHOScIClQq2zQJUYiNjWXJkiVMmTKFli1bcvv27S8Sp/mtI+/xyfxY+L3UBaN/9L/1p3t8pXq0xy/wFap3mVoCQ4JJZ2XNCNfOjGjfRWdwypwBoUj++P2DLrzB76WuGoEoxi/Ho1CAALF26XHp0Jrhf/3J3bt3Wb9+PcePHydHjhzUrVsXFxeXREv0zJkzh6dPnzJnzpwkbzsUKIMudVkKIhexAJoCG4nva3j9+nXWr1/Pxo0byZEjB506dcLV1fWzH5ySJPH69es4ovjxyvHZs2dkypQJW1tbnj59Sp8+fShevLheGHPmzPlNVFFPLseOHaN9+/YcOHCAcuXKJdk+El0WnsWAPzqPWxugCrpwkzLJGFOSJPbu3cvw4cPJnz8/s2bNomjRoqm/iR8MWfhkfixiYuH8TZAkXWYMrZYJa5fjF/iK5cNGoVIqCYkIR635kH7MuU8X/uk7mAblK2NtaUlEdBRuc2eQ3akgLVu2pFKlSgmX4wkKgZdvIFaj+91UpatSkDkDKBRcvHiRRo0acenSJTZv3szSpUs5ceIEJiYmlClThh07dlClSvx9RoBx48YhCALjx49P1q37AWWioghUKHSmziSwBKqhq9CQmJuKVqvlxIkTrF+/nr1791K5cmU6depE06ZNjZdH9ZPxnj9/zuPHj5kzZw6XL1+mWrVqetPqmzdvyJ07t8G9RQcHB+zs7L6ZfSsvLy+aNWvGjh07cHnvQZsAEcAIYDW6l5BP/WqV6EpM5QVmAQ0S6OfKlSsMHTqUwMBAZs2a9UMGoH8usvDJ/HjcfABBIYxf/S8T1i6Pc2pcl56M79YrzrG8bZvE8eqUTE24aQk7d+1ix44dvH79mubNm9OyZUuqV6+e4vimqVOncvToUY4dO8aiRYv4559/OH78ON7e3gwYMIBr164ZNGkOGjSIvHnzxiuUawitVsuECRNYvn07eU+f5lqmTEjEL0kEOtOmBPQDppJAOEQCREREsHv3btavX8/58+dp1qwZHTt2pEaNGmmyChNFkXbt2mFmZsa6desQBIGoqCh8fX3jrBI/XjlqNJoE9xYdHByMVk09Ka5du0a9evVYu3ZtkuLzCqiObsWenGAOC3T/doM+Ovb8+XNGjx7NoUOHmDBhAt27d/+hY/E+B1n4ZH48gsN04icaqAieFAoFOOTUFVB9x/3799m5cyc7duzAx8eHJk2a0LJlS3755Zdk1T/TarXUqlWLhg0bMmLECJYtW8bkyZM5duwY8+fP582bN2zatAlBlCAwSGdCjYklIjwClAqssmaCXNkgnbXBShL+/v60b98epVLJhg0byJo1K37AEmAZEIRO3ETAARgOdAA+N79/QEAAmzZtYv369bx69YoOHTrQsWPHRGscpobIyEiqVatGq1atGDlyZJLtg4ODDQqij48PT548wcbGJsEwjTx58hglTOPu3bvUrFmTBQsW0KpVq0TbRgDOwEMgJdF9lsBCoE1EBH///TcLFiygV69e/Pnnn/oUdzKGkYVP5sfkgS8EvEmZ+AkC2FpByUIJliry9fVl17uV4K1bt2jQoAEtW7akfv36ia4knj59Srly5Th48CBly5ZlzZo1jBo1ir1799KzhxvrJ06jaIZ3e2eG5qxQgIkK8uWELB+CmI8ePUqXLl3o06cPo0aNMrjq0qJbRViS+pwhSeHt7Y27uzsbNmwgY8aM+v1AY9Xbe/78ORUqVGDRokU0bdo01f2IosjLly8N7i36+Pjg7+9P9uzZEwzTyJYtW5Jm1CdPnlCtWjUmTpxI165dk5xTf2A5EJNYZY2PmTABxo+Ho0cxqVEDu0qVqOnoyNSpU8mbN28qv5mfC1n4ZH5MJAnuPYHAt8kSv8iYaBQ21pg7FwdV8kx2AQEB7N69mx07dnD+/Hl++eUXWrRoQePGjQ2662/ZsoWxY8dy5coVrKys2LhxIxPHjuXs0rWYi2CRnOrZCgXkzII2TzYmTJzIypUrWb9+PbVq1UrWnNMaURQ5deoU7u7u7Nq1i3LlytGpUyeaN2/+2YVTL168SMOGDTl27BglS5Y00ozjolar44VpfCyS4eHh2NvbJ2hKjYqKwsXFhYEDB9K/f/8kx4sEsvBuPy8iQpdCrmvXD5U1XF11lTXeC9qjR9CsGbx5A+vWIbi40CkwkLXvwiNkkocsfDI/LpKkMxs+9TfsfQm6xNHABb8nDF34DydOnkyVqSsoKIi9e/eyY8cOTp06RdWqVWnRogVNmzYlc+bM+nZdu3bFzMyMZcuWgSgSdOIsVgiYmSRQWcEAoiCw/Mh+tp3zwN3dnWwfx+t9Q0RFRbF3717c3d3x8PCgUaNGdOrUidq1a6d672nz5s2MHDmS8+fPf5W6cOHh4fHCND7+OSoqiqxZs1KpUqV4ptS8efPGi51bBQwgviOLnk8razRoAP3761aGK1bAL7+QDggkcQclmbjIwifz4/Pe+/JZgK5ckVYEhQBmprq9vCwZEYEGDRrg7OzM5MmTP2u40NBQDhw4wM6dOzl8+DBly5alRYsWNG/eHBsbG0qXLs2sWbNoXro8PAtg4fYtrDm0n5s+D3GtVVcfdrHh6EF6z56m71eURKJiYri0bB0lChREUa4oyhSUOPqaBAYGsnnzZtavX8+zZ89wdXWlU6dOlCpVKsUemGPHjuX48eOcOHECMzMzROAoMBe4h24VZQUUBwaj81xNax/P0NBQateuTcWKFenUqVO8FaOPjw9Pnz7Fzs4ujiCuGzAA30yZDHf6aWWNbdvA3R327NGtAN8Jny2wBV3qOpnkIQufjMw7AgICKF26NJs2baJGjRpG6TMqKorDhw+zc+dO9u/fT+HChSlbtizbtm7lxfYDKESJnadPoBAUHL54jqiY6ATLHK05uI9J61fycMMunVhkywSF8hplnl+Se/fu4e7ujru7O1ZWVnTs2JEOHTqQO3fuZF0viiJt2rTB0sqKcmvWME0QCAfCP2knoBPAjMB4dKnd0kIAIyMjadCgAUWKFGHx4sUJCvn7MI2PxfDvQYOIMlRUWa3Wre7y59dl3QkPh9Kl4cgRcHCII3xW6JIXdE+De/tRkYVPRuYjDh48SK9evbh27Rp2dsbLhA+6LBonT55kx44dRDzxY+ngEdhYfnCISaq+X81BfahRqizjuvbUHVAIUKlUsvckvzVEUcTLy4v169ezfft2SpYsSceOHWnVqlWSXonBERHkPXuWyGrVUCdUgPcjLIGO6DxdjVmSJjY2lmbNmpExY0bWrVuXaAkpQ9iJIkGfXiOK0L49hIbqVncmJjB0KKRLB2PH6tp8JHwW6OL6fjfGDf0kyMInI/MJQ4YMwcfHh507d6ZZILR47Q6KkLg7O4kJn2+AP/naN+Phhp0fUq0pFVDQPo6X5/dKdHQ0Bw4cYP369Zw8eZL69evTqVMn6tatG2/PVQLaA7tFkegUCI0l4AbMM9KctVotrq6uxMbGsm3bNoN7w6Io4u/vz+PHj3n06JH+8/73NxcvIn3siZlQZY1SpcDPT5c2DyAwUCeEI0ZgM2IES9F9JzLJQxY+GZlPiImJoVKlSvTq1Ys+n1QxMBoXbkFU3FDlxIRv0roVHL98kf/mLftwUBB0MYe5v03nltTy5s0btm3bxvr163n48CFt27alU6dOlCtXDkEQ2IxOwCISc/+/fRs6d9Z5QQKULQvz52NVpAh7gNqfOUdRFHFzc+PZs2ds3749nri9/9nHxwcbGxvy58+v/+TLl0//8/CsWdkkCB/SzPXpo9vTO3YMPvaCffMmbgJ2Z2f45x9o0AALa2uuA46feU8/E3JYv4zMJ5iZmbFp0yaqVq2Ki4tL2uQ4lFIWXL/u8AH+6tg1zjGtRsOyRYvZfeUcNjY2cT62trZJ/m5tbZ1i09yXwM7Ojj59+tCnTx8ePXrEhg0b9AH6HTt2ZMMffxBhagoaDeTODadOfXD/b9NG5/6fIwds365zDhFFWLQI2rUj4sYNppNy4QsKCtIL2sOHD9m4cSN+fn7Y2tqSJUsWcufOHUfYqlevrv85sTCOocBOdA45iVbW6NAh7oVKJWTIANbWlEIWvZQiC5+MjAEKFSrE9OnTcXV15cKFC8Yv4ZKC9F6eN6/z4k0grarHfVwLSiX1fm1I/ppVCAsLIywsjNDQUMLCwnj79i1Pnz7V//7p+bCwMCIjI7GwsEi2UCb2u42NDabJ2GtLKfnz52fs2LGMGTOG8+fPM/fkSe5qNLrK8lZWukDu9zRqpHP8uHxZ5/7/Pg2cJOm+74cPAfAAngEfu9JotVr8/PwSNElqtVq9sL148YLQ0FDWrl1LyZIlyZ07d6rDM0qhy6bjDTqRTq4B7skTQJd9549UjfxzIwufjEwCdO/encOHDzN8+HAWLEi4dl+qyGCjC634KJm2VtSiFUWiY2JQKZX6h+naw/tpWa1WHEcYAIVCQf5Sxclvk7rck6IoEh4enqAwfvx7YGBgoufDwsJQqVSpFs5Pf7ewsIizvyoIAhUrViRLxYooJclwBYqXL+H+ffh4hZ4+vc4jUhRh4kRAJ3J9vLxw2LJFL26+vr7Y2dnFMUk2a9ZM//P7xNezZs1ixYoVXL582WjlfWahq6kYlcLrTNCJdyOjzOLnQt7jk5FJhODgYEqVKsWCBQto3Lix8TqOioFLt0CUEk2mHR0TQ7YW9dkxcQa1y5aP24elOTgXM96cPgNJkoiOjk5UGFPyu0ajMSiMN6ZO5aWh0j6fuv9/TEQErF2rW1H9+isARc+cwe3SJb2wOTg4YPFxtXoD/Pvvv0ybNg0PDw99IVljMR/4k3cmz2RgAmQCrgA/1g7vl0EWPhmZJPD09KRly5ZcvnyZnDkTKV6bUq7dhZBPo8+SiVIBBfLoYvl+QNRqtUFhHFqqFN6fZmwx5P7/KaIImTPDnTuQJQvtgQ0pmM/GjRv5448/OHXqVLxCssZiNdAXXTJxQ1U13mMD5AJOAl8+d82PgSx8MjLJYMKECZw+fZojR44Yr/xOaDhcvwdiKv4EzU11q71v0DklLWkF7Pj4QELu/5+i0YCNDXh5QenSDAKSLu+rY8+ePfTu3Zvjx4+neTHX5+hiDRehE0Dt+/9GRyMqlZQ3MWEE0BB5n+pz+Ln+amRkUsmoUaOIjY3l77//Nl6nttZQMK8uED0lqFS6ChI/megB1EAXj6fnt990q7h9++KK3tGjcPUqaLW6leCQITovSCcnrIGKyRzv+PHj9OzZk3379n2RCuY5gcno6vNtRVd2aDbQ68oVag0ahCfQBFn0Phd5xScjk0zelxbav38/5cuXT/qC5PI6GO48BqTEV39Khc6MV6qQLs/oT0gIkJ13jiC+vroMJmZmHwK7QbfHZ2oKY8bogr4tLHRxb9OnQ4kSpEMnLEl9g2fPnqVp06Zs376datWqpc0NJZOHDx9Sq1Ytnj59+lXn8aMgC5+MTArYvn07I0aM4OrVq8Yt9qlWg/9rgm/dw9LCAq1Gg0Kh0BW6lSSwstQFqmdKn2CtwJ+FLuj25wx6diZFTAzOZ85wzNk50X+/lFRP/xJIkoSdnR137tz5KlUpfjR+PluJjMxn0KpVK2rXrk3fvn2N27GJCVGZ02Pv2pSo/DkR8+dm7LoVXIl4C2WLQhknyJzhpxc9gFFAaqMqbUxMyH/gAIULF2bNmjWIBmo13rt3j4YNG7Jo0aJvQvRAF85Rrlw5Ll269LWn8kMgC5+MTAqZM2cOly5dwt3d3aj9njhxglKlSpEuTy6s8uWhYffONOrWiVfhoUYd53unIDoHl8SDD+JjBRxVKNg0ezZ79uxhyZIlVKlSJY6Y+Pr6UqdOHaZMmUKrVq2MOOvPp1y5cly8ePFrT+OHQBY+GZkUYmVlxebNmxk8eDCP3ueCNAL79u2LEytYvXp1unXrRvfu3ZF3JOJSD/gfOtf+pATQCsgA/AdUeHfM2dmZs2fP0qtXLxo3bkzPnj25desWv/zyC8OGDaNbt25pNvfU4uzsLAufkZCFT0YmFZQsWZLRo0fTvn171B8nD04lkiSxb98+mjRpEuf4+PHjefnyJYsXL/7sMX40agJPgAmShPLVKyy1WizROa1YoUvnZQ/MeNfu07B3hUJBt27duHv3LiqVilKlSlGwYEF+//3bLPDj7OzMpUuX5JcgIyALn4xMKhkwYACZMmVi7PsaaZ/BlStXsLa2pmDBgnGOm5iYsHHjRsaPH4+3t/dnj/OjkRGoc/06uStVYp9CwTxgOrrSQ4cAH3RB4Ym5ISkUCi5fvkznzp2JiYmhdOnS/Pfff2k+95SSM2dOBEHg2bNnX3sq3z1yOIiMTCoRBIHVq1dTunRpfvnlF2rXTn2xm0/NnB/j6OjI9OnTad++PRcuXNB5esro2bJlC21bt6aWIFArhddGRUXRuHFjypYtq19V79y5k65du1KhQgVmzZqV7MrwaY0gCHpzZ548eb72dL5r5BWfjMxnkCVLFlavXk2XLl0IDAxMdT979+6NZ+b8mO7du+Po6Miff/6Z6jF+RCRJ0glf27YpvjY2NpZWrVqRK1cuFi1ahCAICIJAy5YtuX37NoULF6Z06dJMmTKF6OjopDv8AsiencZBFj4Zmc+kbt26uLq60qNHj1Ttv/j5+eHr60vlypUTbCMIAv/++y/btm3jyJEjnzPdH4rLly/r9+dSglarpWPHjpiYmLB69ep4dQktLS2ZMGECFy9e5NKlSxQrVox9+/Z99f012cHFOMjCJyNjBKZMmcKLFy9YtGhRiq/dt28fDRs2TLKmW8aMGVm7di3dunXj9evXqZ3qD8WWLVto06ZNnBJGSSGKIr169SIoKIjNmzdjYiip9TscHBzYtWsXixcv5o8//qBhw4bcv3/fGFNPFe9XfIbiD2WSjyx8MjJGwNTUlE2bNjFhwgRu3LiRomsT29/7lFq1atGxY8dUry5/JCRJYuvWrSkyc0qSxJAhQ7hz5w67d+9OdoHhunXrcv36dX755RcqV67MiBEjCAsLS+3UU02WLFlIly6dUcNofkZk4ZORMRKOjo7MmjULV1dXIiOTV1ktPDycM2fOUK9evWSPM2nSJPz8/Pj3339TO9UfgnPnzmFlZUWxYsmvSTh+/HhOnTrFgQMHsLa2TtF4pqamDB06lJs3b/Ly5UucnJzYsGHDF38Bkc2dn48sfDIyRqRz586ULFmSoUOHJqv90aNHqVChAunSpUv2GKampmzYsIHRo0dz9+7d1E71u2fr1q0pMnPOmjWLLVu2cPjwYdKnT5/qcbNnz86aNWvYtm0bc+bMwcXFhatXr6a6v5TyPp5PJvXIwicjY0QEQWDJkiUcPnyYXbt2Jdk+JWbOjylcuDCTJ0+mffv2xMbGpmaq3zWiKLJt27Zkmzn//fdfFi1axNGjR8mSJYtR5lCpUiXOnz9Ply5daNCgAb/99htv3rwxSt+JIacu+3xk4ZORMTLp0qVj48aN9OnTBz8/vwTbabVa9u/fnyrhA+jVqxd58uRh9OjRqZ3qd4unpycZM2bEyckpybabNm1i4sSJHD161OgxeUqlkp49e3Lnzh1UKhVFihRhyZIlaLWpqh2RLMqWLcvVq1fRaDRpNsaPjix8MjJpQMWKFRkwYAAdO3ZM8CF44cIFsmbNioODQ6rGEASBFStWsGHDBo4fP/450/3uSG7s3t69exk8eDCHDh2iQIECaTafDBkysGDBAo4ePcqWLVsoV64cZ86cSZOx0qdPT44cOX5qM/fnIgufjEwaMXLkSARBYPr06QbPJxW0nhwyZcrEmjVr6Nq16xcxs30LaLVatm/fTps2bRJtd/z4cdzc3Ni3b1+KHGA+hxIlSnDy5ElGjhyJq6srHTt25MWLF0YfR3Zw+Txk4ZORSSOUSiXr169n/vz5nD17Nt751O7vfUqdOnVo06YNvXr1+ilCHE6fPk2OHDlwdHRMsM25c+dwdXVl27ZtODs7f8HZ6Vbibdu25e7du9jb21OiRAlmzJhBTEyM0caQhe/zkIVPRiYNyZUrF8uWLaN9+/aEhITojz9+/JjXr19Tvnx5o4wzdepUHj58yKpVq4zS37dMUmbO69ev07RpU9auXUv16tW/4MziYmVlxZQpUzh37hxnzpyhePHiHDx40Ch9y6nLPg9B+hleEWVkvjK//fYbwcHBbNy4EUEQmDdvHjdu3GDlypVGG8Pb25saNWrg6ekZr8rDj4JGoyFHjhycO3eOfPnyxTt/7949atasybx582jduvVXmGHCHDhwgIEDB+Lk5MScOXPInz9/qvuKiIggS5YsvH37FlNTUyPO8udAXvHJyHwBZs+ezY0bN1i7di1gPDPnxxQtWpTx48fToUOHHzbE4eTJk+TNm9eg6Pn6+lK3bl0mT578zYkeQMOGDbl16xZVqlShQoUKjBo1ioiIiFT1ZWVlRf78+VOcJUhGhyx8MjJfAEtLSzZv3szw4cO5fPkyFy5coE6dOkYf5/fffydr1qyMHz/e6H1/CyRk5gwICOCXX35hyJAhdO/e/SvMLHmYmZkxYsQIrl+/zpMnT3BycmLLli2p2puVzZ2pRzZ1ysh8QRYtWsQ///xDwYIFjbbf8ymvXr2iVKlSbNq06avucRmb2NhYsmfPztWrV+PUowsKCqJ69eq0bdv2u4tp9PDwoH///mTIkIH58+dTvHjxZF+7ZMkSvG7dYuKiRYiAHZA+rSb6gyGv+GRkviC///47MTExaRrgnCVLFlauXEnnzp15+/Ztmo2TlkiSRHS0SGSk7hMdLfLff6cpVKhQHNELCwujfv361K9fn1GjRn3FGacOFxcXLl++TOvWralduzYDBgxI8t9MDewAFnbujPvcuRQHSgFZgCLAWiAqjef9vSOv+GRkviBqtZosWbJgbm7O2rVrqVu3bpqNNXDgQAICAti8eXOKyvZ8TTQaiYgILVFR8R9LsbGxBAQ8o1SpgpiYCERHR9OgQQMKFSrE0qVLv5t7TIg3b94wevRodu3axaRJk+jevTtKpTJOm/1AZ0ADJFQb4n3q7blAj7Sa7HeOvOKTkfmCeHp6kj9/fjZs2EC3bt149epVmo01Y8YMbt++zbp169JsDGMhSRJhYVoCAzVERkpIEvE+Jiam5MqVj6AgLW/eqHF1bU/OnDlZvHjxdy96AHZ2dixZsoSDBw+ydu1aKlSowLlz5/TnVwBtgLckLHoA4e8+A4CxaTnh7xh5xScj8wUZOnQotra2jBs3jj///JMbN26wf//+NHtw37x5k1q1anHu3LnPcp9Pa0JCdIKXXGJjY3j+3Jdy5QpiappwIdnvFUmS2LBhAyNGjKBOnTrU+ecfembMmGITpiXwD9A7Deb4PSOv+GRkvhCSJLF37159GMPEiRN5/fo18+fPT7MxixcvzujRo+nQoQNqtTrNxvkcEjJtJoapqRkODo5ERHz/Kz1DCIJAx44duXv3LpmzZaOTRkNUTAz06AH29mBjA6VLw3sHqdhYaNUK8uYFQYD//gMgEhiCbgUo8wFZ+GRkvhD37t0jKiqK0qVLA2BiYsLGjRuZPHky165dS7NxBwwYQIYMGZg0aVKajZFadCZOkejoGIYM6YWzcwEcHTNSp44zJ04c0rfbsGEVlSs7UaBABtq3b0RAwAtAIDpaQqP5cY1WNjY21Jw+HQs7O9BoIHduOHUKQkJg0iRo0waePNE1rloV3N0hW7Y4fQiA+xef+beNLHwyMl+I90HrH5s18+fPz5w5c2jXrl2qg5mTQhAEVq9ezfLly9OsYkBqiY7WiZZWqyFHjlzs3HmMe/de88cf4+nduz3Pnj3h7NnTTJ8+htWrt3P79kvy5MnL77930vcREZF2HrLfAjOBSKUSrKxg/Hjdqk6hgEaNwMEBLl8GU1MYNEgnfp84xES86+PHfT1IObLwych8IRKqxtCxY0ecnZ0ZNGhQmo2dLVs2li9fTqdOnQgODk6zcVJKeLgWSQJLSyuGDRtL7tx5USgU1KnzK3ny5OXGjSscOfI/GjVqSaFCRTE1NWXQoL84d86DJ08eARAVJf2wybm1QIKvKi9fwv37ULRokv0EAAlXhvz5kIVPRuYL8Pr1a27cuEHNmjUNnl+0aBEnT55k+/btaTaHRo0a0bBhQ/r27ZtmY6QESZJIqJZqYOBLHj9+QMGCRdCtVaQ41wHcveutP/aj1mQNBlSGTqjV0KEDdOkChQsn2Y8JEGTcqX3XyMInI/MFOHDgALVr18bc3NzgeVtbWzZu3Mjvv//O06dP02wef//9N1evXmXDhg1pNsbnolar6du3C61bd8LRsTC1atVn797t3L59g6ioKObMmYIgCERFReqvEcUfc8VnEFGETp105s2FC7/2bL5LZOGTkfkCJCcpdfny5Rk6dCgdOnRAk0ZLGEtLSzZu3MigQYPw8fFJkzE+B1EU6d+/K6ampkyZMg8AF5daDBs2lp4921G+fAFy57bH2tqGHDly6a/7AcL4DJIeXaYWPZKk8+x8+RJ27ACT5IVyqIGMxp/ed4scxycjk8bExMSQNWtW7t+/T5YsWRJtK4oidevWxcXFhXHjxqXZnGbPns3OnTs5deoUKpVBY9oXISBAzfsnkCRJDB7cEz8/X9av34uFhYXBax49uk/duuW5fNmH9OkzAJA5swqV6sdUvxrAqfe/9OkD167BsWNgbR23YUyMThgLFIBVq6BaNTAzA0HAAXiEzsNTRl7xycikOadOnaJIkSJJih6AQqFg3bp1LFmyJE09MAcPHoylpSVTp05NszGS4tatW3h4HNOXUBo5sh8PH95l7dpdcUQvOjqau3dvIUkSfn5P+eOP33Fz66cXPZWKH1b0AP4ArEQRfH1h2TKd8GXLphM+a2t4b7YuVAgsLOD5c6hXT/ezry9W7/r4cb+hVCDJyMikKf369ZOmTp2aomv27t0r2dvbS0FBQWk0K0l6/vy5lDVrVsnLyyvNxviU169fS3PmzJFy5colKRQKKV8+R8nHJ1S6cOGBBEhmZmaSpaWV/rNw4Rrpzp1XkpNTMcnCwlLKnDmr1K/fcOnZsyjpxYtYyd8/VoqM1H6x+X9pIiIipNHjxknCy5c619VUfCwlSQr7CnP/lpFNnTIyaYgkSeTNm5cDBw5QNBlu5x/Tv39/Xr58yZYtW9Ispdnu3bsZOnQoV69exdbWNk3G0Gg0HD58mMWLF3P06FG0Wi2CINCwYUPmzp2LrW0e1OrUPYYEAbJmVf0QuTo/RpIkdu/ezeDBg6lQoQINFy7kt8yZU5WybA7QKw3m+D0jC5+MTBpy48YNmjVrxqNHj1L8cI6OjqZ8+fIMHDiQHj3SLs9+7969iY6OZu3atYiiRFSUrhTQ+8pJggCmpgJWVgpMTZO/O3Lr1i3WrFnDqlWriI2NJSoqCmtra/r168eff/6J9bs9Ko1G4vVrDal5EmXMqMTM7Mfasbl37x4DBgzAz8+PBQsWUKtWLUCXpHoAyS85ZAkMBSamzTS/a2Thk5FJQyZPnszr16+ZO3duqq6/ffs21atXx8PDg8LJiNdKDREREVSt6sLKlZvJnt0h0bZKJdjaKjE3Nyw2QUFBbNq0iZUrV/Lo0SM0Gg0xMTHky5ePSZMm0apVq3ildgDUaok3b1ImfhkyJDyP75Hw8HAmTZrEypUrGTVqFP369cPkE69NuSyRcfhx/q+RkfkGSU4YQ2IUKVKESZMm4erqSkxMjBFn9gFzc0v27j1Nxow5kmyr1cLbt1rCwz+kCdNoNPzvf/+jdevW2NvbM3PmTG7evElUVBQuLi5cuHCB+/fv07ZtW4OiB2BiIpA5swozs4RXxRqNGlHUYmIiYGf344ieJEls2rSJwoULExAQwK1btxg8eHA80QNoBLwE1gDl0QWmW6ETOxN0hWgXAa+QRS8x5BWfjEwaERAQgJOTEy9fvsTU1DTV/UiSRIsWLcibNy9z5swx4gx1gd+vX2tITUH48HB//v13Ae7u7lhbWxMVFUVgYCAqlYqePXsyYsQIsmfPnuJ+tVqJyEiRqCgRUdQdEwTw9r6Kh8cRxo0bnfLJfqPcvHmTfv36ERoaysKFC6lSpUqKrg9Fl5FFRBenl974U/wh+TFemWRkvkH2799PvXr1Pkv0QJdkesWKFWzfvp2D78vQGInQUC2RkYlXRti7dxvVqhXH0TEj1auX4ODBPQCoVOm5ffsu4eHhvHjxAkEQmDdvnt60mxrRA1AqBWxslGTJYkK2bLpP1qwm5Mhhy7JlixHfq+F3THBwMAMHDqR27dq0a9eOS5cupVj0AGyBvEA+ZNFLCbLwycikEZ9r5vwYOzs73N3d6d69OwEBAXHOiaKuNI9aLaHVJj9hs86RRUq0MoK//3P69+/K+PF/c//+G8aMmU7fvp15/VpXOb5ECWdKlizJrl27ePr0KX369Ekw8PxzKVy4MJkyZcLT0zNN+v8SiKLI6tWrcXJyIjo6mtu3b/Pbb78laAKWSRtkU6eMTBoQFRVF1qxZefLkCRkzGi9Z1JgxY7hw4QIHDhxArRaIiBCJjZX0KbskSWcWtLJSYGmpQKlMeM8sIkJLaKjh1VPt2mUYMmQ02bPnokuX5ty8+Vx/rlixHKxZs5Ny5Soiilpy5DD7YuEEkydP5tWrV2lavDetuHTpEv369QNg4cKFlCtX7ivP6OdFXvHJyKQBx48fp0yZMkYVPYBx48aRJUsOnjwJJThYS2ys7r1Vkvgo9ReEh4u8eqUhJEST4AowMtKw6H1cGaFkybI4Ohbm8OF9aLVaDh7cg5mZGUWKFAdAqVTq5/AlaN26Ndu3b0ebmk3Jr8Tr16/p3bs3jRs3pnfv3nh5ecmi95X5ekn6ZGR+YBKqvfe5aLUKZsxYiiAokuX6rzNlasmQQRlvVWZIOz6tjADQqlVH+vbtTExMNCYmpvz77yYsLa0S7SetKFSoEFmyZMHT05Nq1ap9uYFTgVarZfny5YwdOxZXV1fu3LlD+vTpv/a0ZJBXfDIyRkcURfbv32+0/b33qNUSb99qEYTk/9lKEsTESISExFenT1dNhiojnD59nClT/mTHjmP4+kawc+dxhg3rw61b1/T9f2natGnD1q1bv/zAKcDLywtnZ2c2bdrEsWPHmDdvnix63xCy8MnIGJkrV65ga2uLo6OjUfsNCdESHZ2wB+azZ0/IkcOUAgUy6D9z5kwBdCs/tVoiKCiIxYsXU758eQIDX+r7liSJIUN68fr1K5Yv36KPIfP2vk6FClUpWbIsCoWCUqXKUbq0Mx4eJwDdfuKXzhb2LZs7AwIC6Nq1K23atGH48OH8999/lChR4mtPS+YTZOGTkTEyaWHm/OC1mbAH5nvu3g3k4cO3PHz4lsGDRwG61dz//nccBwcH3N3dsbW15dKl8/q6fwlVRihVqhznz3vqV3g3b17lwgVPnJx0e3ySpAs+/5I4OjqSI0cOPDw8vui4iaFWq5k7dy7Fixcna9as3LlzB1dX1x8uh+iPgrzHJyNjZPbt22d0r8OICN3qxtLSimHDxuqP16nzK3ny5OXGjSuUKFEmwesVCgUlS1bAwsKSV69e4e/vj719furXb/Ku/t1yzMzMKFkyt/6amTMX0aJFe4YOHUOvXq4EBr7Ezi4z/fuPoEaNOgC8fOmHrW0WVCqrhIZOE96bO2vUqPFFxzXEyZMn6d+/v16M0yq1nIzxkMMZZGSMyNOnTylTpgwBAQFGLfD68qUaQ3HbgYEvKV++AEeOXMTc3JwKFQqSLVsOBEHAxaU2Y8ZMx84uEwAREeEMH94HR0d7fvvtNxwcHHj1Sp1q5xRR1LJ06d8sW7aAvn370q9fP+zs7D7jLpPPo0ePqFy5Ms+fP/9qhXT9/PwYNmwY586dY86cOTRr1kxe4X0nyKZOGRkjsn//fho2bGj0h7Gh19NPPTAzZszEwYNnuXDhIYcOnSMiIox+/bro25uZmbFmzVpmzpyJg4MuGbWtbeoDp01NlUycOBoPDw+ePXuGo6MjgwcP5tmzZ6nuM7nkz5+fXLlycfr06TQf61NiYmKYNm0aJUuWpGDBgty+fZvmzZvLovcdIQufjIwRSaswhk8x5IFpZWVNyZJlUalUZM6clSlT5nHq1FHCwkIBMDExwcQkbvo0c3MFNjYpewxIkoRCAXZ2ujp4hQoVYsWKFdy8eROlUknJkiXp3r07d+/eNc7NJkCbNm3Ytm1bmo7xKYcOHaJ48eKcPXuWCxcuMHHiRCwtLb/oHGQ+H1n4ZGSMRFhYGF5eXtStW9fofSs++ktNyAPzU96vQN7vZkRFRXH06GHu3r0bJ6jd2lpJunTJexTExsbw7JkPmTIpUSjirnBy5szJrFmzePjwIfny5aN69eq0aNGCCxcupORWk03r1q3ZsWOH3kEnLfHx8aFZs2b069ePOXPmsHfvXvLnz5/m48qkDbLwycgYiaNHj1KpUqU0qWRubv5BZBLywLxy5QIPH95DFEWCgt4wevRgKleujq1tOgBUKhV79mynQYMGZM6cmaZNmzJz5ky8vLxQKjVkyaLC2lpBeHgYWq1aH6bw/r+mpgJ2dqb07t2WDRvcE5xrxowZGT16ND4+PtSqVYs2bdpQq1Ytjhw5kuw8oskhX7582Nvbc+rUKaP1+SlRUVGMHz+ecuXKUb58eW7dusWvv/6aZuPJfBlk5xYZGSPRtWtXypUrp8/HaCw0Gg07d+6hfPl6BAYGUL68I2ZmZiiVH/YRZ85chCAomD59LK9fv8LGxpZq1WozevQ0smTJBoCFhUD69Lprnj9/jqenp/5z9+5dSpUqRdmyZVmzZg23bz8gQwadU4wg6EIWVCqdAl69epW6dety7do1cubMmeT81Wo1mzdvZsaMGZiamjJy5EhatmxplMTMf//9Nw8fPmTZsmWf3dfHSJLEnj17GDx4MM7OzsyaNYs8efIYdQyZr4csfDIyRkCr1ZItWzYuXbqEvb29UfqMiYlh3bp1TJ8+ndy5c7NkyUZsbe1QKFJuqBFFkSxZTBOMuQsPD+f8+fMsXrwYDw8PoqOjyZUrF1WrVqVKlSpUqVKF/Pnz682n48aN49KlS+zfvz/ZTh26WML/MW3aNAIDA/njjz/o3LkzZmZmKb6f9zx58gRnZ2f8/f2N5lB07949Bg4cyLNnz1iwYAG1atUySr8y3w6yqVNGxgicO3eOHDlyGEX0oqKiWLBgAQUKFGDHjh2MGjUKR0dHXF0bExub8irsWq2GTZtWsWzZogRNjdbW1tSuXRsTExOmTp1KUFAQGzZsoHjx4hw8eJAaNWqQPXt2WrZsyZw5c6hbty5+fn6sXbs22fNQKBQ0btwYT09PVq1axe7du3FwcODvv/8mNDQ0xfcFkDdvXvLly8fJkydTdf3HhIeHM3LkSKpUqaJf0cqi92Mir/hkZIzAyJEjUalUTJ48OdV9hIWFsWTJEubMmUP58uUpV64chw4d0te5c3NzI0OGzAQFaZOdI1MQwMxM4M2bJ7Ru3RpHR0eWL19OunTp4rVVq9VkyZKF27dvxysiK0kST58+xdPTkzNnzuDp6cmDBw/QaDT89ttvNGjQgEqVKhnsNzGuX7/OzJkzOXz4ML1792bAgAFkzZo1RX0sXrwMO7sc1KxZXx/rqFDo9kWtrJSJlmZ6f29btmxh+PDh1KxZkxkzZqS6iK7M94EsfDIyqUSSNICu6kGRIkVYs2YN5cuXT3E/b9++ZcGCBSxYsIDKlSuTLVs29uzZQ9GiRenbty9NmjSJY8bTJavWIIpJJ4m2stKFKwiCQHR0NIMHD+bYsWNs3bqV0qVLx2l74sQJRo4cmWwvzODgYPr378/Zs2fJlSsXly9fJl++fFSpUkVvIs2TJ0+yTKGPHz9m1qxZbN68GVdXV4YNG6aPNUwIjUaXfDsmRiQ2NgYzM3OD7UxNBWxtlQbNvLdu3aJfv34EBwezcOFCqlatmqx7l/m+kU2dMjLJRJK0qKPuE/56AyH+cwgNmE9owD+8fTGP/r3LUKZUytzbX716xZ9//kn+/Pnx9PSkdOnSeHh4YGpqysmTJzl+/DgtWrSIt3dlYiKQObOKjBmVmJl9/DCXUKvVKBRgY6Mga1YVtrYfyhGZm5uzZMkSJk6cSN26dVm6dGkc02dKK8anT5+eVatWYWNjQ5cuXQgKCmL58uU4OjqyY8cOKlSoQJ48eWjXrh0LFy7k6tWrCSaWzpcvH4sXL+bOnTukS5eOcuXK0aFDB27cuGGwfWysyOvXmndFeIUERU/XVuLNGw0xMR9S3wQHBzNo0CC91+nly5dl0fuJkFd8MjLJICbiBtFhpwEJpNh45zUaCZXKBKVJZizT/4pClbDJ7/nz58yaNYs1a9ZQrFgx/P39MTc3p2/fvnTs2BEbG5sUzU2SJL2JL18+B86dO0f27NkSvebevXu0bt2aYsWKsWzZMqytrXF0dGT79u2UKlUqReNfv36dX375hStXrpA794dcn5Ik8ejRozjm0efPn1OhQgX9qrBChQpYW1vH6zMkJIRly5Yxd+5cSpcuzciRI3FxcQF0K943bzQpLokkCJAhg4JNm9bz559/0rhxY6ZMmULmzJlT1pHMd48sfDIyiSBJEtGhp4iNvA4kJ1BaAMEUa7s2KE2yxDnj4+PDjBkz2LRpE3nz5uXp06fUqVOHvn37Uq1aNaOkvKpUqRIzZ87Ui0RiREVFMWDAAE6fPs2MGTMYMGAAvr6+qZrHxIkT8fLy4uDBg4le/+bNG7y8vPRieO3aNQoXLqz3HK1atSo5cuTQt4+OjmbdunXMnDmTbNmyMXLkSMqXr0dkZAx//tkfD48TBAcHkTdvfv78cxK1atVn586N/PFHX30foigSHR3FwYNnyZEjJz17tmLhwoU4Ozun+D5lfgxk4ZORSYTo8AvEhJ8FKYXZQQRzbDJ1QqGy5d69e0yZMoVdu3aRMWNGYmJi6NOnD7169YrzkDcGnTt3pmbNmnTr1i3Z16xfv54+ffpQvnx5Tpw4kSrhU6vVVKhQgb59+9KjR49kXxcdHc3ly5fjxBTa2Njo9wirVq1KkSJFEEWRHTt2sHfvASZNmo8kSSxePJu2bTuTM2cejh8/yO+/d+LEiSvkzp03zhhbtqxj7typeHndQavVkDmzGebmnx9DKPP9IgufjEwCiNpQwl6tAuLvS/k+C2LYnzu5cNkXM1MVTX8tzrSJTVGp3j9QBaJiMtJrwE6OHz+OUqmkePHiDBw4kObNmyeYZuxzmThxIjExMUyZMiVF15UtW5bAwEBq1KjBkiVLsLJKeZmhmzdvUqtWrXgmz5QgSRL37t3Tm0bPnDnD69evqVy5MlWqVKFVq+5YW2cwWIW+du0yDBkyml9/bRHneKtWdahUqRpDh44B3megkSuy/czIzi0yMgkQE3E1wXPD/txJpkzW3Ls6Fo+jg/E895gVa7w+aiEhEMDNG+dxdXXVr2batGmTZqIHuiKtDx48SNE1b9684eHDh1y9ehWFQoGzszPe3t4pHvu9sLu5uaU6NZkgCBQuXBg3NzdWr17NgwcPuHv3Lj169CA4OBgLC1uDohcY+JLHjx9QsGCROMf9/Hw5d86D1q076o/FxkqIovy+/zMjC5+MjAEkSUNs5A0MrfYAfJ8G0bxxSczNTciaxZbaNQpx9/7LOG1UKhOuXdzIihUrKF68+BeYNRQoUICHDx+m6JoDBw5Qq1Yt7OzsWLNmDcOHD6d69eopCk5/z4gRI3j9+jUrVqxI8bUJkTVrVlq0aMG0aTNQqeK/NHxanuljtm1zp0KFquTJ8yE0QhAwWNtQ5udBFj4ZGQNoY18ker6PW1V27LlGZGQsL/xDOHbyLrVrForTRqUEQXyUltOMR4ECBXjw4EGKVlyfhjF069aN//77j+nTp9O9e3ciIyOT3ZeJiQlr1qzhzz//5OnTpymae1JI0oeE2e8xVJ7pY7Zv30Dr1p2MOg+Z7x9Z+GRkDCCKiT/sq1TKz917AeQuNJoiZSdRqmRuGtUvFq+dJKU8xdjnkCFDBszMzHj16lWy2sfGxnLkyBEaNmwY53ixYsW4ePEisbGxVKhQIUW19YoXL86QIUM+y+RpCIUibsB+UuWZLlzwIiDgBY0axd3zMySgMj8XsvDJyBhEeveJjyiKtHRdTuOGxXnxcCqPb00gODiKcZP/l0A/X5b3q77k4OHhQaFChciWLX7cn7W1NevXr2fAgAG4uLiwYcOGZM/hjz/+4O3btyxfvjzZ1ySFIMStS5hQeab3bNu2nl9/bY61ddy4SIUibj8yPx/yP7+MjAEEwRwwvCx4+zYKvxfB9OxWBTMzFRkzWtGhrTNHT9wx0I+pgR7SFkdHx2Tv8yWVrUUQBHr27MmxY8eYMGECvXr1IioqKsl+VSoVa9asYdSoUfj6+iZ77knx/PlDoqOj8PPzZf365Xh7X6dkydwUKJCBAgUysHPnRkAXJrFv33aDZk5LS4VRYiZlvl9k4ZORMYDKNDtIhh1b7OyssM+TkVVrz6LRaAkOiWLTtksUK/JpTJ4ClZlxShSlhOQ6uEiSlOw0ZSVLluTSpUuEhoZSqVIl7t+/n+Q1RYsWZciQIfTo0eOzTJ6iKLJ7924qVKhA795d+H979x0dVbX+f/x9pqT3QgARpZckICDwA6SGooCF7xVEilyICDE0cxGEK4oYql5EUOx6FemooIAUqQqCNIMESCGU0EyAQJi0aef3R0y4MYWUmRCY57VWlsnMnnN2lkM+s8/Zez96vZ5atR7g4kUjp0/fJDExLf/r//5vEJC7PdvJk6l07Fi4uoKbm/zZc3TyDhCiCIrGBb1LA4ob9S35dBg/7TxJvdDptGw/G51Ow6w3nvhbKw3O7g/bva9/V9olDSdOnMBkMtGsWbNSHdfLy4vly5czatQoOnTowMqVK2/7mpdffpn09PRyFYo1mUwsWbKE0NBQoqOjeeWVV9i/fx9eXuVbDqIo4Oam3LZag7j3yQJ2IYphMf2J4coKSrdVWWEaXSCegc/ZtlOl8NtvvxEREcGhQ4dKbDd37lzOnTvH+++/X+ZzHD58mAEDBtCzZ0/mz5+Pi0vxm0QfP36cTp06cfDgQR588MHbHjsrK4svvviCefPmUadOHaZOnUr37t3zL0+qqkpamuWvTadLH2LOzgq+vlq5zClkxCdEcbT6IHTOD2IyleezoQ5X7ztTxDRvxHe7z7Rlrcbwv1q2bMmhQ4dISUmhffv2nDpV/LKNpk2b8vLLLxMeHo61hAV06enpzJs3j7p167Jp0yaWL1/Ojh076NGjR4GwUpTcANu3bxcmU+ENw4vi6iqhJ26R4BOiGKqqMn32Lk4mXEGlLHs76nD17oXOqZbd+lYSX19f9Ho9qampxba5cuUKf/zxB126dCn3eby9vVm9ejXDhw+nXbt2fPPNN8W2/de//oXBYCjykmdqairTpk2jbt26xMTEsGXLFr7//nvatWtX7PFWrVrFlClj8fVVcHXNDTNFKfgFucVoAwJ0+PjoJPREPgk+IYpgtVp58cUX+fnnvQS3mIiTSwNAW/KOH4oeFCfc/J7Eya1xCQ3t73YzOzdu3EhYWFiJlyhLQ1EUxo4dy4YNG5g4cSLjxo0jJ6fw2sW8WZ7Tpk3j9OnTACQnJzNhwgQaNWpESkoK+/fvZ+nSpbfd5ebChQuMGzeOJUuW4Onpho+PjqAgHT4+Wry8cr98fLQEBenw9dUVWYBWODYJPiH+xmKxEB4ezrFjx9iyZQu+fgG4+fbBI3AYW7YnYzbnlh7K/0KHRuuHq1cYXkGj0Ts/eKd/hduu5avIZc6itG7dmsOHD3Pu3Dk6duyYH27/q0mTJkyaNImBAwcyYsQImjdvjk6n49ixY3z00UfUq3f7Qr5Wq5Xhw4cTGRlZoKyQRqPg4qLBzS33y8VFg0YjgSeKJluUC/E/TCYTw4YNIyUlhU2bNhWoUnAtzcyosf8lOfkMbi45qNYcULRoNO5odD53rtNFKGlJg9FoZOvWrbz33ns2Paevry/fffcdCxYsoG3btnzyySc8+eST+c8fOXKEAwcOcPjwYQICAkhISMDf379M51i8eDE3btxg6tSpNu27cCwy4hPiL0ajkWeeeYYbN26wfv36QqV5Vq9eTZ8+ffD09Plr4kttdE73VbnQg5KXNOzatYvGjRsTFBRk8/MqisJLL73E999/z/jx44mKimL79u089thj9O3bl3bt2rFv3z7279/PjRs3ynTskydPMn36dJYsWYJOJ5/ZRflJ8AlB7k4f/fr1A+C7774r8t7X0qVLGTRoUGV3rVxKGvGtX7/eppc5i9K2bVvmzp3Ll19+Se/evenSpQtJSUlERUXRqlUrXnnlFUaMGJE/y1NVVYxGK1lZVjIzc/9rNt+alWoymRgyZAjR0dE0bNjQrn0X9z5ZxyccXkZGBk8++SSBgYF89dVXRdbLO336NG3atOHixYt2radnK9euXaNOnTpcv369wGxGVVWpV68ea9euLfXC9bKwWCysWbOG2bNnY7VamTx5MsnJybzzzjt8/vnn9OnTJ79dx44dGTbsnwweHE5GhpW//yVSVdDrFTw8NMye/QYHDx5k/fr1MjtTVJgEn3Bo6enp9O3bl3r16vHpp5+i1Ra9bGH27NkkJyezePHiSu5h+fn5+REXF0dgYGD+Y7GxsfTu3ZszZ87YNECMRiNLlixh7ty5BAQEMHXqVPr06ZN/jj179jBw4EAGDRpEdHQ0er2eU6fOAV64uroWWVw2j9Vq4fz5c9Su7UONGtVs1mfhuORSp3BYaWlp9OzZk5CQED777LNiQ09V1bvqMmeeopY05M3mtFXoZWRksGDBAurWrcuqVav45JNP2LNnD3379i1wjg4dOnD48GGOHj1K165dOX8+FTe3Gri5uZcYegAajZZatR5AUXyxWORzuqg4CT7hkK5cuUK3bt1o374977//PpoS6tT88ccfGAwG2rdvX4k9rLiiljTYahlDWloab775JnXq1OGXX35h3bp1bN68mc6dOxcbqoGBgWzYsIHnnhuB0Vi2qhUajQZVhatXzTat8ScckwSfcDiXL1+mS5cu9O7dm//85z+3Hf0sXbqUZ599tsRwrIr+PsElNTWV2NjYCu3WcunSJSZNmkS9evVISkpi9+7drFmzhlatWpXq9RqNhn/84zlcXFzJyckhKuoFWreuT4MGfvTo0Zrt2zflt83MzGTKlLEEB9egUaMA+vXrhtUKWVkSfKJiZE6wcCjnz58nLCyMoUOH8uqrr962vdVqZfny5WzYUFSR2arLalXp2vUxUlKukZZmRqOB338/yWOP9cbZ2bnMxzt9+jRvvfUWK1asYMiQIRw5coQHHih7ySWLRcVoVFEUBYvFTM2atfj225+4777abNv2I6NGDWL79sPcf/+DTJoUgdlsZvfuo/j4+BEbG4OqgsFgkdJCokJkcotwGGfOnCEsLIyIiAgmTpxYqtf8/PPPREZGcvToUTv3zjZMJhWDwUJ2torVakGjuXXfMjs7C71ej6enHnd3LTrd7e/zxcbGMmfOHDZu3MioUaOYMGEC1aqVf4JJerqZjIzi/+SEhbUkKupVGjUKpnfv9hw6dBpPT68CbRQF/Py0ODlJ+InykXeOcAgJCQl07tyZqKioUoce3F1r9zIyLFy5YiY7OzdY/jf0AFxcXNFqdWRmqn+1K37j0f379/PUU0/RrVs3mjZtSlJSErNmzapQ6AEYjcWHXmrqnyQlJdCwYVOOHPmNWrVq8/bbMwgOrkG3bi3YsOFbIHeZQ/kqZgiRS4JP3POOHz9O165dee2114iMjCz164xGI2vWrOHZZ5+1Y+9sw2CwkJ5e0g7aBakqpKVZCoSfqqps27aNsLAwBgwYQPfu3Tl9+jRTpkzB29vbJv0sbpNvk8lEZOQw+vcfSoMGjbl06QInT8bi6enFkSNnmTnzXcaPDych4USJxxGiNCT4xD0tJiaGsLAw5syZQ3h4eJleu2XLFpo0aVKue1mVyWi0cvNmbhKMGTOMhx6qTcOG/jzySFOWLv08v93PP2+nY8cQ6tb15umne3D+/FmuX7dgNFpYu3Ytbdu2JTIykqFDh5KQkMCYMWNwc3OzaV+LmkdktVoZO/afODk5MXPmu0Du6FSv1zNhwlScnJxo164T7dt3Zteun4o9jhClJcEn7lkHDhygV69eLFq0iCFDhpT59XfLZc680AMYO3YS+/cnEB9/lS+++JZ5817n6NHDXL16heefH8CkSdM5fvxPmjVrxejRg7FYLHz22TKio6OZPHkysbGx/POfuSFkD3+vmKCqKlFRL3DlSgqffLIyf1ecJk1KLk0klRdERcjkFnFP2rNnD/369eOzzz4r17o1g8FArVq1SExMJCAgwA49tA2LRSUlxVzkc4mJcTz9dA9mzPgP6ek3WLnyK374YTcAmZkZhITUYPPm36hbtwE1azpVynKN7Gwr169b8rcnmzw5ktjYGFau3IS7u0d+O5PJROfOzejffwhjx07m8OHfGDy4Lxs37qVBg8YEBekk/ES5yYhP3HN27NhBv379+Prrr8u9WHvt2rU88sgjVTr0IHdCy99NmTKWunW96dQplGrVqhMW9hhxcccJDr61N6ebmzsPPFCX+Pjj6HRasrMrp7/OzrfC6vz5syxZ8gmxsTE0b34/9ev7Ur++L99+uwy9Xs8XX6xh+/ZNNGoUwMsvj2bhws9p0KAxLi6KhJ6oEFnHJ+4pmzZt4rnnnmP16tV07ty53MdZtmxZuS6PVjZzEYO92bMXER29gIMH9/Hrr7twcnImI8OAv3/BEPf09MZgMKCqYDZbqYzPwYqi4O6uwWCwUqvWA1y8aCy2baNGwfzww8+FHvfwKHprOSFKS0Z84p6xbt06hg0bxrp16yoUeqmpqezdu7dAEdWqymot+k6FVqulbdsOXLp0gS+//Ah3dw8MhpsF2hgM6Xh4ePx1HLt3NZ+Hh4byltPz8NCg18toT1SMBJ+4J6xatYpRo0axceNG2rVrV+Fj9enTp1Ah2qrodtutmc1mzp5NolGjpsTG3lqEn5mZwZkzSTRs2BSAytyNTVEU/P11ZQo/RQE3t9wSRUJUlLyLxF3vq6++YsKECWzZsqXUe0aWZNmyZQwePNgGPbO//w2PK1dSWLt2JRkZBiwWCzt3bmHt2pV06NCFxx57kri4WDZs+Jbs7Gzmz4+madNQGjRojKKAVlu5oyiNRiEgQIebm4KiFL88QVFyQ9nLS4O3t05q8QmbkFmd4q728ccfM2PGDLZu3UqTJk0qfLy7reCs2aySmmoCFK5eTWXkyIEcP34Uq9VKrVq1CQ8fw+DBuesXd+/exr//PZ4LF87RokUbFiz4lPvvfxDgjs6SVFWVrCyVjAwLlr/m6ihKbhFad3cNTk6KBJ6wKQk+cddauHAh8+fP56effqJ+/fo2OeasWbM4f/78XVFw9tKlS8ybN48ePfrTokXrch/H1VXBx0fmuQnHIZc6xV1p7ty5LFy4kF27dtks9PIKzlb1y5yXLl1iwoQJBAcHo6oqDz3UsELHc3eXWZLCsUjwibuKqqq88cYb/Pe//2XXrl023U7s6NGjZGRkVHhyjL1cvHiR8ePHExwcjKIoxMbGsmDBAmrWDMDdvXyXAr28ZJakcDwSfOKuoaoqU6ZM4ZtvvmHnzp3cd999Nj3+smXLqmTB2QsXLjBu3DhCQkLQarXExsbyzjvvUKNGjfw2np5a3N2VMu1h6eWlkdGecEhyYV/cFVRVZcKECfzyyy/s2LEDf39/mx4/r+Dsxo0bbXrcirhw4QJz5sxh6dKlDB8+nOPHj1O9evUi2yqKgpeXDmfn3A2rSyrb4+ycuyxA6tkJRyXBJ6o8q9VKREQER48eZdu2bfj4+Nj8HL/88gs+Pj6EhITY/Nhldf78eebMmcOyZcsYMWIEJ06cICgoqFSvdXbW4OyswWxWycy0YDbnliDKmyXp5qap9KULQlQ1EnyiSjObzYSHh3PmzBm2bNmCp6enXc5TFdbuJScnM2fOHJYvX054eHiZAu/vdLrcEaAQojD5lyGqLJPJxJAhQ0hLS+PHH3+0eW24PHkFZw8dOmSX499OcnIys2fPZsWKFTz//POcPHmywpXOhRDFk4v8okrKycmhf//+ZGZm8v3339st9AA2b958RwrOnjt3joiICJo3b46HhwcnT55k3rx5EnpC2JkEn6hysrKyeOqpp9DpdHzzzTe4uLjY9XyVfZnz7NmzjB49moceeggvLy/i4uIk8ISoRBJ8okoxGAz06dMHf39/VqxYYbdK4Hlu3rzJxo0befrpp+16HsgNvFGjRtGiRQt8fHyIi4tj7ty5BAYG2v3cQohbJPhElXHjxg0effRR6taty5dffomuvLVrymDdunV07NjRrgVn8wKvZcuW+Pn5ER8fz5w5cyTwhLhDJPhElXDt2jW6d+9O8+bN+fjjj9FqK2dhtT0vc545c4YXXniBli1b4u/vT1xcHLNnz67yVd2FuNdJ8Ik7LjU1lW7dutG5c2fee++9Sts5JSUlhb179/LEE0/Y9LinT59m5MiRtGrVisDAQOLj45k1a5YEnhBVhASfuKMuXbpE586deeKJJ3jrrbcqtfzM6tWr6du3r80KziYlJfH888/z8MMPExQURHx8PDNnzrT5LjNCiIqR4BN3zLlz5+jUqRNDhgxhxowZlV5zbenSpQwaNKjCx0lKSiI8PJzWrVtTo0YNEhISiI6OlsATooqSBezCZlTVitWcitWaBYBG44pGF4CiFL5fl5SURFhYGOPGjeOll16q7K6SlJREYmIiPXr0KPcxTp06xcyZM1m3bh2RkZEkJCTg5+dnw14KIexBgk9UmNWSgTHzKMaMw6hYgLyRmwpocHJ7CGf35mi0uduNxcXF0aNHD6ZMmUJERMQd6fOKFSvo379/uaqsJyYmMnPmTH744QciIyNJTEzE19fXDr0UQtiDBJ8oN1VVycn4jZybv/71iKXIdsaMgxgzDuLs8TCJZ73p1etRoqOjGT58uN37aDFfxZhxBIspBVXNAUWPRuvH4YObeelfs8p0rMTERKKjo1m/fj1jxowhISFBAk+Iu5Ciqmrx9UuEKEHWje0Ys/4A1Vyq9larhu9+iMHVuyfPPlvxe2slMeWcIefmHiymK+QG8q23uapCVrYJd49quHi2Q+/SuMT7i3n37DZs2MCYMWMYP368BJ4QdzEZ8YlyyTEcKlPoAWg0Vp7q2ww37zp27Blk39xHjmE/UHTfFAXcXPWoljSybmzFnHMWV++eKErBuV7x8fFER0ezceNGxo4dS2Jiol1KIgkhKpfM6hRlpqomsg17igy9uIQ/ebz/B9Ru9Cot2s/mhx//KPC8VquSY9iPas2xS9+yDQdKDL1CVBOmrDiybvxE3sWPuLg4hg4dSvv27alfvz6JiYm8/vrrEnpC3CMk+ESZmbJOFvm42Wxh0PAv6NW9KaePz2DBvKcZNWYZiadSCzZUFIyZsTbvl8X0JzmGvXz8+U66PLqAag9OJmLCivznjUYzz438ktA2M/GpOZGf9ybm9RxT9knOJu1k6NChPPLIIzRs2JBTp07x2muvSeAJcY+R4BNllmM4AKqp0OPxiSlcvpxO5Aud0Go1dH6kAW1b12HFN3+rc6eayck4gK1vL2cbfgPVQvXq3kwc350hA9sUavP/2tTh40WDCKr2t4K2qolL536kUaNGJCYmMm3aNLy9vW3aPyFE1SD3+ESZqFYjVsuNop8rIsdUVeXEyctFHCcL1ZqJorXNrilWaxbm7FOAyhO9QwH4/WgyFy7d6quTk44XR3YCQKst/JmvaeOatHlkMFq9BJ4Q9zIZ8YkyUdVsinvbNKxfjYAADxYu3onJZGH7zjj27EsiK8tYqK3ZovLr3p38+uuvHD16lMTERC5evMiNGzcwmQqPJm/HlBXHrfWD5WXFmBlTwWMIIao6GfGJMir+s5Jer2Xp5/9k0qtrWbB4By2a1aLf481xcir8NjOZjCxe/AGnTl8hMzOTjIwMMjMz879XFAV3d3fc3Nxwc3O77fe9uvnQqllFa/epWMzXK3gMIURVJ8EnykTRuFDcQnWAkKY12fjti/k/93x8Ec8OeLhQO1cXJ75euuav4xWkqiomk6nIQCzue73ORvcL1cKjUyHEvUWCT5SJoujQOtXGYjxb5PPHjl+kft1ArFaVz77cy+WUdAYNaF2onVYfVGTo5Z5DwcnJCScnp1LPqMxK/xljxm+l/j2KU1yfhBD3Dgk+UWYuHq3JSLtY5MzOlWsO8dXy3zCbLLRrW4e1K0bh7Py3t5mix9mj8IzLitDqA0HRg2rCbLZgNluxWFQsFivZ2SZ0Og06nZacHHP+bFKT0UJ2tglnZ91fO7do0epr2LRfQoiqR7YsE2Wmqio3Uz5GtRrK9XpFccEzKKLQTikV65OZ9D8/ANXI7Lc3M3f+1gLPT47qwZSJvQhtM5Pk82kFnovZP5UH7vcDtHhWG4nGRjNNhRBVkwSfKBez8QIZV9dQ6h1S8ulw9+uHzrm2zfuUeGIZ3m7JRU6mKQ2dc13c/frZuFdCiKpGljOIctE53Yebb1/KdrVch6vPozYPvWvXrjFy5EgGDHoDjabsZYby+ubs0c6m/RJCVE0SfKLc9C71cPcfwM0MHdnZZopeR6f8VQrIB3f/f+Dk2shm51dVlSVLlhAcHIyLiws7dv6Gd7X+lP3WtQ4X7+7onKrbrG9CiKpLLnWKCrFYLAQHB/P5p/N4KFiLKefUrUkvih6dcx2c3R9Gq69eYumfsoqLiyMiIoLr16/z0Ucf0br1rZmj5pzzZKR9B6qFkpZe5H7u0+Dq3Qsnt8Y265sQomqTWZ2iQlauXElAQADtOjyeH2x5n6VsGXR5srOzmTVrFosXL2batGlERkai0xV8G+uca+EZOAJjZgzGjCO5VeFVM7k1+RRQcts7uYbi7N4Cjc7H5v0UQlRdMuIT5ZY32lu0aBE9evSw+/m2bt3Kiy++SPPmzXn33Xe57777bvsaVbVizknCar6G1ZqDonFCo/VG71IPRSnv/UAhxN1MRnyi3FauXIm/vz/du3e363kuX75MVFQUv/76K++99x59+vQp9WsVRYPepb4deyeEuNvI5BZRLhaLhTfffJPp06fb5ZImgNVq5YMPPiA0NJTatWtz7NixMoWeEEIURUZ8olxWrVqFn5+f3UZ7v//+O6NHj0an07Fjxw5CQkLsch4hhOOREZ8oM4vFwowZM+wy2jMYDERFRdGrVy9GjhzJ7t27JfSEEDYlwSfKzB6jPVVVWbt2LU2bNuXatWscO3aM8PBwNBp5iwohbEtmdYoysVgshISEsHDhQpvN5Dx79ixjx44lPj6eDz/8kC5dutjkuEIIURT5OC3KxJajPZPJxFtvvUWrVq1o06YNMTExEnpCCLuTyS2i1PLu7b377rsVvre3d+9eRo8eTY0aNdi3bx/168uSAyFE5ZDgE6W2atUqfH19K3SJ89q1a0yZMoX169czf/58BgwYYLflEEIIURS51ClKpaLr9lRV5euvvyY4OBi9Xk9sbCzPPPOMhJ4QotLJiE+UyurVq/Hx8SnXaC8uLo4XX3yRa9eusW7dOtq0sW31dSGEKAsZ8YnbKu+6vezsbF5//XU6dOjA448/zoEDByT0hBB3nIz4xG2VZ7T3008/ERERQbNmzfj999+pVauWHXsohBClJ+v4RIksFguhoaEsWLCAnj173rb9n3/+SVRUFHv37mXRokX07du3EnophBClJ5c6RYlWr16Nt7f3bUd7VquVDz/8kNDQUO6//36OHTsmoSeEqJLkUqdAteZgzjmD1ZoFWFEUF3TOtVBxZ8aMGbzzzjsl3tuLiYlh1KhRaLVatm3bRmhoaOV1XgghykiCz4FZTKnkZBzClBUHigZUK6Dmf38lTUvXTg2LHe0ZDAamT5/OV199xaxZsxgxYoTsrSmEqPLkHp8DUlWV7PRdGDNjAOtfX4VZrSqqqsHJpSbufv+HonHKf27t2rWMGzeOrl278vbbbxMYGFg5nRdCiAqS4HMwqqqSdWNz7igPcylfpUWj88HDfzDnki8ybtw44uLi+OCDD+jatas9uyuEEDYn16UcTE7GwTKGHoAFq/k6sUfepVWrVrRu3ZqYmBgJPSHEXUlGfA5EVc2k//kBqEY+/vwXlq06yPGTl/jHUy34YMHA/Ha7fk5g4tRvOX/hOq1a1mbxgmeoXcuPnBwLGZbu1KnX8g7+FkIIUTEy4nMgpuwEIPdzTvXq3kwc350hAwvupHL1agZDn/+Sf096lNPHZ9CiWS1GjP4aAGdnHUH+KZXdbSGEsCkJPgeSYzgAqgmAJ3qH0vexEPx83Qq0+eHHP2jcMIinHm+Oi4ueVyb25Njxi8QnpAAqpqw4VKvxDvReCCFsQ4LPgVjNV2/b5kTcZUKCa+b/7O7mTJ0H/DkRfzn3AUWD1ZJmry4KIYTdSfA5CFW1kHeZsyQZGUa8PF0KPObl6YrBkHPrWNZsW3dPCCEqjQSfw9BQmuBzd3fipqFgsN00ZOPh4XzrAUX2PRBC3L0k+ByEoigoistt2zVpVJ1jsZfyf87IzOH0mas0aVg99wHVikbjYa9uCiGE3UnwORC9WwigBcBstpCdbcJiUbFYrGRnmzCbLfR9LIQTcZdZt+Eo2dkm5s3fSnDTGjRsUA0Ajc4Xjc77Dv4WQghRMbKOz4FYzencTP0csDD77c3Mnb+1wPOTo3owZWIvdu6O5+V/f0fyhTRatajN4gUDeeB+P1D0uHr3xMm18Z35BYQQwgYk+ByM4epqLMZkSnO/rxDFGa+gCBRFa/N+CSFEZZFLnQ7Gzac3isYVKL7MUNF0uPv1k9ATQtz1JPgcjEbrjrv/QBSNG6X/36/DzfcJdE732bNrQghRKeRSp4OyWjLJvrkLU1Y8KEr+ji635I7stE41cfXqglZfrfI7KYQQdiDB5+BUaw7GzOMYs46h5ldgd0bnUhdntxZodF53uotCCGFTEnxCCCEcitzjE0II4VAk+IQQQjgUCT4hhBAORYJPCCGEQ5HgE0II4VAk+IQQQjgUCT4hhBAORYJPCCGEQ5HgE0II4VAk+IQQQjiU/w+BTtz9XtK+GgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "G.remove_edge(3, 9)\n",
    "assert G.degree(3) == G.degree(12)\n",
    "nx.draw(G, with_labels=True, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Removal of the road has partially isolated _Town 3_ as well as its neighboring towns. Hence, we can expect _Town 12_ to garner more traffic than _Town 3_ , even though their degrees are equal. In fact, we can quantitate these differences in traffic using random simulations.\n",
    "\n",
    "### 19.1.1 Measuring Centrality Using Traffic Simulations\n",
    "\n",
    "Lets simulate the random path of a single car. The car will start its journey in a random town `i`. Afterwards, the driver will randomly select one of the  `G.degree(i)` roads that cut through town.  The process will repeat itself until the car has driven through 10 towns.\n",
    "\n",
    "**Listing 19. 5 Simulating the random route of a single car**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After driving randomly, the car has reached Town 24.\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "def random_drive(num_stops=10):\n",
    "    town = np.random.choice(G.nodes)\n",
    "    for _ in range(num_stops):\n",
    "        town = np.random.choice(G[town])\n",
    "        \n",
    "    return town\n",
    "\n",
    "destination = random_drive()\n",
    "print(f\"After driving randomly, the car has reached Town {destination}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we’ll repeat this simulation with 20,000 cars.\n",
    "\n",
    "**Listing 19. 6 Simulating traffic using 20,000 cars**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We ran a 2.56 second simulation.\n",
      "Town 12 has the most traffic.\n",
      "There are 1015 cars within that town.\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "np.random.seed(0)\n",
    "car_counts = np.zeros(len(G.nodes))\n",
    "num_cars = 20000\n",
    "\n",
    "start_time = time.time()\n",
    "for _ in range(num_cars):\n",
    "    destination = random_drive()\n",
    "    car_counts[destination] += 1\n",
    "\n",
    "central_town = car_counts.argmax()\n",
    "traffic = car_counts[central_town]\n",
    "running_time = time.time() - start_time\n",
    "print(f\"We ran a {running_time:.2f} second simulation.\")\n",
    "print(f\"Town {central_town} has the most traffic.\")\n",
    "print(f\"There are {traffic:.0f} cars within that town.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Town 12_ has the most traffic, with over 1000 cars. This is not surprising, given that _Town 12_ has the highest degree centrality, along with _Town 3_. Based on our previous discussion, we expect _Town 12_ to have more heavy traffic than _Town 3_.\n",
    "\n",
    "**Listing 19. 7 Checking the traffic in _Town 3_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 934 cars in Town 3.\n"
     ]
    }
   ],
   "source": [
    "print(f\"There are {car_counts[3]:.0f} cars in Town 3.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, _Town 3_ has less than 1000 cars. We should note that car-counts can be cumbersome to compare, especially when `num_cars` is large. Hence, it's preferable to replace these direct counts with probabilities, through division by the simulation count.\n",
    "\n",
    "**Listing 19. 8 Converting traffic counts to probabilities**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of winding up in Town 12 is 0.051.\n",
      "The probability of winding up in Town 3 is 0.047.\n"
     ]
    }
   ],
   "source": [
    "probabilities = car_counts / num_cars\n",
    "for i in [12, 3]:\n",
    "    prob = probabilities[i]\n",
    "    print(f\"The probability of winding up in Town {i} is {prob:.3f}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "W’ve shown that _Town 12_ is more central than _Town 3_. Unfortunately, our simulation process is slow, and doesn’t scale well to larger graphs. In the next sub-subsection we’ll show how to compute the traffic probabilities more efficiently using straightforward matrix multiplication.\n",
    "\n",
    "##  19. 2 Computing Travel Probabilities Using Matrix Multiplication\n",
    "\n",
    "Our traffic simulation can be modeled mathematically, using matrices and vectors. We’ll break down this process into simple, manageable parts. Consider for instance, a car that is about to leave _Town 0_ for one of the neighboring towns. The probability of traveling from _Town 0_ to any neighboring town is `1 / G.degree(0)`. It is also equal to `1 / M[:,0].sum()`, where `M` is the adjacency matrix.\n",
    "\n",
    "**Listing 19. 9 Computing the probability of travel to a neighboring town**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of traveling from Town 0 to one of its 5 neighboring towns is 0.2\n"
     ]
    }
   ],
   "source": [
    "prob_travel = 1 / G.degree(0)\n",
    "assert prob_travel == 1 / adjacency_matrix[:,0].sum()\n",
    "print(\"The probability of traveling from Town 0 to one of its \"\n",
    "      f\"{G.degree(0)} neighboring towns is {prob_travel}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we’re in _Town 0_ and _Town i_ is a neighboring town, then there’s a 20% chance of us traveling from _Town 0_ to _Town i_. Of course, if _Town i_ is not a neighboring town, then the probability drops to zero. We can track the probabilities for every possible `i` using a vector `v`. This vector is called a **transition vector**, since it tracks the probability of transitioning from  _Town 0_  to other towns. \n",
    "\n",
    "**Listing 19. 10 Computing a transition vector**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.  0.  0.2 0.2 0.  0.2 0.2 0.  0.  0.  0.  0.  0.2 0.  0.  0.  0.\n",
      " 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0. ]\n"
     ]
    }
   ],
   "source": [
    "transition_vector = np.array([0.2 if i in G[0] else 0 for i in G.nodes])\n",
    "\n",
    "adjacency_matrix = nx.to_numpy_array(G)\n",
    "v2 = np.array([1 if i in G[0] else 0 for i in G.nodes]) * 0.2\n",
    "v3 = adjacency_matrix[:,0] * 0.2\n",
    "v4 = adjacency_matrix[:,0] / adjacency_matrix[:,0].sum()\n",
    "\n",
    "for v in [v2, v3, v4]:\n",
    "    assert np.array_equal(transition_vector, v)\n",
    "\n",
    "print(transition_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.array_equal(transition_vector,\n",
    "                      adjacency_matrix[:,0] / adjacency_matrix[:,0].sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Executing `M / M.sum(axis=0)` will divide each column of the adjacency matrix by the associated degree. The end-result is a matrix whose columns correspond to transition vectors. This matrix is referred to as a **transition matrix**.\n",
    "\n",
    "**Listing 19. 11 Computing a transition matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_matrix = adjacency_matrix / adjacency_matrix.sum(axis=0)\n",
    "assert np.array_equal(transition_vector, transition_matrix[:,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our transition matrix allows us to compute the traveling probability to every town in just a few lines of code. If we want to know the probability of winding up in _Town i_ after 10 stops, then we simply need to:\n",
    "\n",
    "1. Initialize a vector `v` where `v` equals `np.ones(31) / 31`.\n",
    "2. Update `v` to equal `transition_matrix @ v` over 10 iterations and return `v[i]`.\n",
    "\n",
    "**Listing 19. 12 Computing travel probabilities using the transition matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of winding up in Town 12 is 0.051.\n",
      "The probability of winding up in Town 3 is 0.047.\n"
     ]
    }
   ],
   "source": [
    "v = np.ones(31) / 31\n",
    "for _ in range(10):\n",
    "    v = transition_matrix @ v\n",
    "    \n",
    "for i in [12, 3]:\n",
    "    print(f\"The probability of winding up in Town {i} is {v[i]:.3f}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can model traffic-flow using a series of matrix multiplications. These multiplications serve as the basis for **PageRank centrality**. PageRank centrality is easy to compute, but not so easy to derive. Nonetheless, with basic probability theory, we can demonstrate why repeated `transition_matrix` multiplications directly yield the travel probabilities.\n",
    "\n",
    "### 19.2.1 Deriving PageRank Centrality from Probability Theory\n",
    "\n",
    "`transition_matrix[i][j]` equals the probability of traveling from _Town j_ directly to _Town i_. Of course, that probability assumes that our car is located in _Town j_. Generally, if the probability of our current location is `p`, then the probability of travel from the current location `j` to new location `i` equals `p * transition_matrix[i][j]`. Suppose a car begins its journey in a random town, and travels one town over. What is the probability that the car will travel from _Town 3_ to _Town 0_ ? Well, the car can start the journey in anyone of 31 different towns. Consequently the probability of traveling from _Town 3_ to _Town 0_ is `transition_matrix[0][3] / 31`. \n",
    "\n",
    "\n",
    "**Listing 19. 13 Computing a travel-likelihood from a random starting location**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of starting in Town 3 and driving to Town 0 is 0.004\n"
     ]
    }
   ],
   "source": [
    "prob = transition_matrix[0][3] / 31\n",
    "print(\"Probability of starting in Town 3 and driving to Town 0 is \"\n",
    "      f\"{prob:.2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability of that particular path is very low. However, there are multiple paths to reaching _Town 0_ from a random starting location. Lets print all non-zero instances of  `transition_matrix[0][i] / 31` for every possible _Town i_.\n",
    "\n",
    "**Listing 19. 14 Computing travel likelihoods of random paths leading to _Town 0_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of starting in Town 3 and driving to Town 0 is 0.004\n",
      "Probability of starting in Town 4 and driving to Town 0 is 0.0054\n",
      "Probability of starting in Town 6 and driving to Town 0 is 0.0065\n",
      "Probability of starting in Town 7 and driving to Town 0 is 0.0046\n",
      "Probability of starting in Town 13 and driving to Town 0 is 0.0054\n",
      "\n",
      "All remaining transition probabilities are 0.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(31):\n",
    "    prob = transition_matrix[0][i] / 31\n",
    "    if not prob:\n",
    "        continue\n",
    "        \n",
    "    print(f\"Probability of starting in Town {i} and driving to Town 0 is \"\n",
    "          f\"{prob:.2}\")\n",
    "    \n",
    "print(\"\\nAll remaining transition probabilities are 0.0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Five different routes take us to _Town 0_. Each route has a different probability. The sum of these probabilities equals the likelihood of starting at any random town and traveling directly to _Town 0_.\n",
    "\n",
    "**Listing 19. 15 Computing the probability that the first stop is _Town 0_**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of making our first stop in Town 0: 0.026\n",
      "Frequency with which our first stop is Town 0: 0.026\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "prob = sum(transition_matrix[0][i] / 31 for i in range(31))\n",
    "frequency = np.mean([random_drive(num_stops=1) == 0\n",
    "                     for _ in range(50000)])\n",
    "\n",
    "print(f\"Probability of making our first stop in Town 0: {prob:.3f}\")\n",
    "print(f\"Frequency with which our first stop is Town 0: {frequency:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our computed probability is consistent with the observed frequency. It’s worth noting that the probability can be computed more concisely as vector dot product operation. We just need to run `transition_matrix[0] @ v`, where `v` is a 31-element vector whose elements all equal `1 / 31`.\n",
    "\n",
    "**Listing 19. 16 Computing a travel probability using a vector dot product**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.ones(31) / 31\n",
    "assert transition_matrix[0] @ v == prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Executing `transition_matrix[i] @ v` will return the likelihood of making our first stop in _Town i_. We can compute this likelihood for every town by `[transition_matrix[i] @ v for i in range(31)`. Of course, this operation is equivalent to the matrix product between `transition_matrix` and `v`. Hence, `transition_vector @ v` returns all first-stop probabilities. \n",
    "\n",
    "\n",
    "**Listing 19. 17 Computing all first stop probabilities**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First stop probabilities:\n",
      "[0.026 0.033 0.045 0.046 0.033 0.019 0.025 0.038 0.033 0.031 0.019 0.041\n",
      " 0.052 0.03  0.036 0.019 0.031 0.039 0.023 0.031 0.027 0.019 0.018 0.044\n",
      " 0.038 0.046 0.015 0.045 0.04  0.035 0.023]\n",
      "\n",
      "Probability of making our first stop in Town 12: 0.052\n",
      "Frequency with which our first stop is Town 12: 0.052\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "stop_1_probabilities = transition_matrix @ v\n",
    "prob = stop_1_probabilities[12]\n",
    "frequency = np.mean([random_drive(num_stops=1) == 12\n",
    "                     for _ in range(50000)])\n",
    "\n",
    "print('First stop probabilities:')\n",
    "print(np.round(stop_1_probabilities, 3))\n",
    "print(f\"\\nProbability of making our first stop in Town 12: {prob:.3f}\")\n",
    "print(f\"Frequency with which our first stop is Town 12: {frequency:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We’ve established that `transition_matrix @ v` returns a vector of first stop probabilities. Furthermore, we can easily show that `transition_matrix[i] @ stop_1_probabilities` returns a vector of second-stop probabilities. However,  `stop_1_probabilities` is  equal to `transition_matrix @ v`. Consequently, the second-stop probabilities are also equal to `transition_matrix @ transition_matrix @ v`. \n",
    "\n",
    "**Listing 19. 18 Computing all second stop probabilities**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Second stop probabilities:\n",
      "[0.027 0.033 0.038 0.043 0.033 0.023 0.028 0.039 0.039 0.026 0.021 0.032\n",
      " 0.048 0.034 0.039 0.023 0.032 0.041 0.023 0.029 0.025 0.024 0.023 0.04\n",
      " 0.029 0.043 0.021 0.036 0.036 0.042 0.031]\n",
      "\n",
      "Probability of making our second stop in Town 12: 0.048\n",
      "Frequency with which our second stop is Town 12: 0.048\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "stop_2_probabilities = transition_matrix @ transition_matrix @ v\n",
    "prob = stop_2_probabilities[12]\n",
    "frequency = np.mean([random_drive(num_stops=2) == 12\n",
    "                     for _ in range(50000)])\n",
    "\n",
    "print('Second stop probabilities:')\n",
    "print(np.round(stop_2_probabilities, 3))\n",
    "print(f\"\\nProbability of making our second stop in Town 12: {prob:.3f}\")\n",
    "print(f\"Frequency with which our second stop is Town 12: {frequency:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We were able to derive our second-stop probabilities directly from our first stop probabilities. If we repeat our derivation, then we can easily show that `stop_3_probabilities` equals  `transition_matrix @ stop_2_probabilities`.  Of course, this vector also equals `M @ M @ M @ v`, where `M` is the transition matrix.  We can repeat this process to compute the fourth-stop probabilities, and then fifth-stop probabilities, and eventually the Nth stop-probabilities.  \n",
    "\n",
    "**Listing 19. 19 Computing the Nth-stop probabilities**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tenth stop probabilities:\n",
      "[0.029 0.035 0.041 0.047 0.035 0.023 0.029 0.041 0.034 0.021 0.014 0.028\n",
      " 0.051 0.038 0.044 0.025 0.037 0.045 0.02  0.026 0.02  0.02  0.019 0.039\n",
      " 0.026 0.047 0.02  0.04  0.04  0.04  0.027]\n",
      "\n",
      "Probability of making our tenth stop in Town 12: 0.051\n"
     ]
    }
   ],
   "source": [
    "def compute_stop_likelihoods(M, num_stops):\n",
    "    v = np.ones(M.shape[0]) / M.shape[0]\n",
    "    for _ in range(num_stops):\n",
    "        v = M @ v\n",
    "        \n",
    "    return v\n",
    "    \n",
    "\n",
    "stop_10_probabilities = compute_stop_likelihoods(transition_matrix, 10)\n",
    "prob = stop_10_probabilities[12]\n",
    "print('Tenth stop probabilities:')\n",
    "print(np.round(stop_10_probabilities, 3))\n",
    "print(f\"\\nProbability of making our tenth stop in Town 12: {prob:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we’ve discussed, our iterative matrix multiplications form the basis for PageRank centrality. \n",
    "\n",
    "### 19.2.2 Computing PageRank Centrality Using NetworkX\n",
    "A function to compute PageRank centrality is included in NetworkX.\n",
    "\n",
    "**Listing 19. 20 Computing PageRank centrality using NetworkX**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The PageRank centrality of Town 12 is 0.048.\n"
     ]
    }
   ],
   "source": [
    "centrality = nx.pagerank(G)[12]\n",
    "print(f\"The PageRank centrality of Town 12 is {centrality:.3f}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The printed PageRank value is 0.048, which is slightly lower than expected. This is due to the concept of _teleportation_ which is built into the PageRank algorithm. The algorithm assumes that a traveller will teleport to random node in 15% of all transitions. Imagine that in 15% of our town visits, we call for a helicopter, which takes us to a totally random town. Hence, 15% of the time, we’ll fly from _Town i_ to _Town j_ with a probability of `1 / 31`. In the remaining 85% of instances, we’ll drive from _Town i_ to _Town j_ with a probability of `transition_matrix[j][i]`. Consequently, the actual probability of travel from _i_ to _j_ equals the weighted mean of `transition_matrix[j][i]` and `1 / 31`.  Taking the weighted across all elements of the transition matrix will produce an entirely new transition matrix. Below, we’ll update our transition matrix, and recompute the _Town 12’s_ travel probability. \n",
    "\n",
    "**Listing 19. 21 Incorporating randomized teleportation into our model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of winding up in Town 12 is 0.048.\n"
     ]
    }
   ],
   "source": [
    "new_matrix = 0.85 * transition_matrix + 0.15 / 31\n",
    "stop_10_probabilities = compute_stop_likelihoods(new_matrix, 10)\n",
    "\n",
    "prob = stop_10_probabilities[12]\n",
    "print(f\"The probability of winding up in Town 12 is {prob:.3f}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our new output is consistent with the NetworkX result. Will that output remain consistent if we raise the number of stops from 10 to 1000? Lets find out.\n",
    "\n",
    "**Listing 19. 22 Computing the probability after 1000 stops**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of winding up in Town 12 is 0.048.\n"
     ]
    }
   ],
   "source": [
    "prob = compute_stop_likelihoods(new_matrix, 1000)[12]\n",
    "print(f\"The probability of winding up in Town 12 is {prob:.3f}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The centrality remains consistent 0.048. Ten iterations are usually sufficient to achieve PageRank convergence. Transition / Markov matrices have mathematical properties that tie together much of this book’s material. Markov matrices bridge graph theory with probability theory and matrix theory. However, that’s not all. Markov matrices can also be leveraged to cluster network data, using a procedure called **Markov clustering**.\n",
    "\n",
    "## 19. 3 Community Detection Using Markov Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graph `G` represents a network of towns. Some of these fall into localized counties. Thus far, we’ve visualized the counties by mapping colors to individual county ids. What if we didn’t know the county ids? How would we identify the counties? Lets ponder this question by visualizing `G` without any sort of color mapping.\n",
    "\n",
    "**Listing 19. 23 Plotting `G` without county-based coloring**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "nx.draw(G)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our plotted graph has neither colors nor labels. Still, we can spot potential counties. They look like tightly connected clusters of nodes within the network. In graph theory, such clusters are formally referred to as **communities**. The process of uncovering communities in graphs is called **community detection**, or **graph clustering**. Some graph clustering algorithms depend on simulations of traffic-flow.\n",
    "\n",
    "Suppose we drive from _Town i_ to _Town j_ and then to _Town k_. Based on our network structure, _Towns i_ and _k_ are more likely to be in the same county, We will confirm this statement shortly. However, first we’ll need to compute the probability of transition from _Town i_ to _Town k_ after two stops. This probability is called the **stochastic flow**, or **flow** for short.  We’ll need to calculate the flow between each pair of towns, and store that output in a **flow matrix**. The flow matrix is equal to `transition_matrix @ transition_matrix`. Hence, a random simulation should approximate the product of the transition matrix with itself.\n",
    "\n",
    "**Listing 19. 24 Comparing computed flow to random simulations**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "flow_matrix = transition_matrix @ transition_matrix\n",
    "\n",
    "simulated_flow_matrix = np.zeros((31, 31))\n",
    "num_simulations = 10000\n",
    "for town_i in range(31):\n",
    "    for _ in range(num_simulations):\n",
    "        town_j = np.random.choice(G[town_i])\n",
    "        town_k = np.random.choice(G[town_j])\n",
    "        simulated_flow_matrix[town_k][town_i] += 1\n",
    "\n",
    "simulated_flow_matrix /= num_simulations\n",
    "assert np.allclose(flow_matrix, simulated_flow_matrix, atol=1e-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We believe that the average flow between _Towns i_ and _j_ is higher if `G.nodes[i]['county_id']` equals `G.nodes[j]['country_id']`. We can confirm by separating all flows into two lists; `county_flows` and `between_county_flows`. The two lists will track intra-county flows and inter-county flows, respectively. We’ll plot a histogram for each of the lists. We’ll also compare their mean flow values. \n",
    "\n",
    "\n",
    "**Listing 19. 25 Comparing intra and inter-county flow distributions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean flow within a county: 0.116\n",
      "Mean flow between different counties: 0.042\n",
      "The minimum intra-county flow is approximately 0.042\n",
      "132 inter-county flows fall below that threshold.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def compare_flow_distributions():\n",
    "    county_flows = [] \n",
    "    between_county_flows = []\n",
    "    for i in range(31):\n",
    "        county = G.nodes[i]['county_id']\n",
    "        nonzero_indices = np.nonzero(flow_matrix[:,i])[0]\n",
    "        for j in nonzero_indices:\n",
    "            flow = flow_matrix[j][i]\n",
    "            \n",
    "            if county == G.nodes[j]['county_id']:\n",
    "                county_flows.append(flow)\n",
    "            else:\n",
    "                between_county_flows.append(flow)\n",
    "    \n",
    "    mean_intra_flow = np.mean(county_flows)\n",
    "    mean_inter_flow = np.mean(between_county_flows)\n",
    "    print(f\"Mean flow within a county: {mean_intra_flow:.3f}\")\n",
    "    print(f\"Mean flow between different counties: {mean_inter_flow:.3f}\")\n",
    "    \n",
    "    threshold = min(county_flows)\n",
    "    num_below = len([flow for flow in between_county_flows\n",
    "                     if flow < threshold])\n",
    "    print(f\"The minimum intra-county flow is approximately {threshold:.3f}\")\n",
    "    print(f\"{num_below} inter-county flows fall below that threshold.\")\n",
    "    \n",
    "    plt.hist(county_flows, bins='auto',  alpha=0.5, \n",
    "             label='Intra-County Flow')\n",
    "    plt.hist(between_county_flows,  bins='auto', alpha=0.5, \n",
    "             label='Inter-County Flow')\n",
    "    plt.axvline(threshold, linestyle='--', color='k',\n",
    "                label='Intra-County Threshold')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    \n",
    "compare_flow_distributions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Flows below a threshold of approximately 0.04 are guaranteed to represent inter-county values. Of course, we’re only able to observe this threshold due to our advance knowledge of county identities. In a real-word scenario, the actual county ids would not be known. We’d be forced to assume that the cutoff is a low-value, like 0.01. Suppose we made that assumption with our data. How many non-zero inter-county flows are less than 0.01?\n",
    "\n",
    "**Listing 19. 26 Decreasing the separation threshold**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 inter-county flows fall below a threshold of 0.01\n"
     ]
    }
   ],
   "source": [
    "num_below = np.count_nonzero((flow_matrix > 0.0) & (flow_matrix < 0.01))\n",
    "print(f\"{num_below} inter-county flows fall below a threshold of 0.01\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "None of the flow values fall below the stringent threshold of 0.01. We need to manipulate the flow distribution in order to exaggerate the difference between large and small values. This manipulation can be carried out with a simple process called **inflation**. Inflation is intended to influence the values of a vector while keeping its mean constant. We can inflate a vector `v` by executing `v2 = v **2` and subsequently dividing `v2` by `v2.sum()`.\n",
    "\n",
    "**Listing 19. 27 Exaggerating value differences through vector inflation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.array([0.7, 0.3])\n",
    "v2 = v ** 2\n",
    "v2 /= v2.sum()\n",
    "assert v.mean() == round(v2.mean(), 10)\n",
    "assert v2[0] > v[0]\n",
    "assert v2[1] < v[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like vector `v`, the columns of our flow matrix are vectors whose elements sum to 1. We can inflate each column by squaring its elements, and then dividing by the subsequent column sum.\n",
    "\n",
    "**Listing 19. 28 Exaggerating flow differences through vector inflation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean flow within a county: 0.146\n",
      "Mean flow between different counties: 0.020\n",
      "The minimum intra-county flow is approximately 0.012\n",
      "118 inter-county flows fall below that threshold.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def inflate(matrix):\n",
    "    matrix = matrix ** 2\n",
    "    return matrix / matrix.sum(axis=0)\n",
    "\n",
    "flow_matrix = inflate(flow_matrix)\n",
    "compare_flow_distributions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our threshold has decreased from 0.042 to 0.012. However, it still remains above 0.01. How do we further exaggerate the difference between inter-county and intra-county edges? Well, setting the flow matrix to equal `inflate(flow_matrix @ flow_matrix)` will cause the threshold to drastically decrease. \n",
    "\n",
    "**Listing 19. 29 Inflating the product of `flow_matrix` with itself**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean flow within a county: 0.159\n",
      "Mean flow between different counties: 0.004\n",
      "The minimum intra-county flow is approximately 0.001\n",
      "541 inter-county flows fall below that threshold.\n"
     ]
    },
    {
     "data": {
      "image/png": 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9hg8fDsCSJUvo2LEj7dq148Ybb+TQoUPB/e3evRuAwsLC4IcQx40bx4033khWVhbnnnsukydPBmDMmDF89tln+Hw+Ro8ezdChQ5k/f34ww5AhQ3jllVcq/d58+eWX9O7dm/bt29O7d2+2bNlCSUkJ5557Ls459u7dS61atcjPzwf8n1rdtGlTpY8TT5FcLdPIzE4NPD4RuBT4xMyahKx2NbA28PgVYJCZ1TWzZkALYFVUU4eYN29esPeFiBwpkpa/u3fv5uGHH2bx4sWsWbOGjIwM/vCHPwT3kZqayvLlyxk0aFBw2b59+9i3bx/Nmzcvc8yDBw8yYsQI5syZw0cffcThw4eDFz6U55NPPuGNN95g1apV/P73v+eHH35g4sSJwVH4o48+ekRHyG+++YYVK1bQr1+/Mvsq/YXg8/kYOXJkmddHjRrFsGHD+PDDDxkyZAh33XUXKSkptGzZkvXr17N8+XIuvPBCli1bxqFDhyguLuZnP/tZRO95oohkzr0J8Gxg3r0WMNc5t8DMnjMzH/4pl83ArQDOuXVmNhdYDxwGRsbqShnwNzcSkfBKW/4CwZa/R9904t1332X9+vXBrof//ve/6datW/D1cFeiOecwCzcDCxs2bKBZs2bBW+0NHz6cp556ipycnHKz/vznP6du3brUrVuXxo0bh72j08UXX8zIkSPZuXMnL730EgMGDKB27bJlrPQXwrGsXLmSl156CYChQ4fy29/+FvCP0PPz8/niiy8YO3Ys06dP5+KLLz5mf51EVmFxd859CJTp7uOcG1rONuOB8dWLFpnSu7iMGDGiJg4n4imRtPx1znHZZZfxwgsvhN3HSSedBMANN9zA+++/z1lnncXChQs56aST+Pzzz4N3Kwrd37GEtvw9Vrvf8rKCvxjPmjWL2bNn8+c///mYx6qM0l9UPXv2ZOrUqWzbto0HH3yQRx99lLy8PDIzM6NynJrk+Za/M2fODBZ4EYlMaBvdrl278s477wTnlA8cOMDGjWVv7D1jxgyKioqCPV3Gjh3LyJEj+fbbbwH/Le+mTZvGeeedx+bNm4P7e+6554LtdNPT04M94F988cVK5Sw1YsQIcnNzAWjTpk1lf3QAunfvzuzZswGYNWtW8K+ZLl26sGLFCmrVqkVqaio+n49nnnnGczfqgCRoPyCS0CK4dDEejm75O3PmTAYPHhw88fnwww8Hp1WO5fbbb2f//v106tSJOnXqUKdOHe6++25SU1OZMWMG11xzDYcPH6ZTp07B+6w+8MAD3HTTTUyYMIEuXbpUmLNBgwb06NGDtm3b0rdvXx599FHOOOMMzj//fK666qoq//yTJ0/mxhtv5NFHH6VRo0bBefy6deuSlpZG165dAf9IvvReq16jlr8iUaSWv7F34MAB2rVrx5o1azx3A43qqGzLX89Py4jI8WPx4sWcd9553HnnncdVYa8KTcuIiGdceumlbNmyJd4xPMHzxV0N+yXRlHeZoEhVVGX63PPTMvXq1at2fwyRaElNTWXPnj1R/xi+HL+cc+zZs4fU1NRKbef5kXtp34nKNBYSiZWmTZtSXFyM+iVJNKWmpgY/jBYpzxf3uXPnAirukhjq1KlDs2bN4h1DxPvTMiIiUpaKu4hIElJxFxFJQiruIiJJyPMnVNV2QESkLI3cRUSSkOeL+6RJk5g0aVK8Y4iIJBTPF/cFCxawYMGCeMcQEUkokdxDNdXMVpnZB2a2zsx+H1h+upktMrNPA99PC9lmrJltMrMNZtYnlj+AiIiUFcnI/RBwiXOuA+ADLjezrsAYYIlzrgWwJPAcM2sNDALaAJcDUwL3XxURkRpSYXF3fvsDT+sEvhzQH3g2sPxZ4KrA4/7AbOfcIefcF8AmoHM0Q4uISPkimnM3sxQzKwJ2Aoucc+8BZzjntgMEvjcOrH42sDVk8+LAsqP3mW1mhWZWWJ0mSyeeeCInnnhilbcXEUlGEV3n7pwrAXxmdirwspm1LWf1cI2sy/Q/dc5NA6aB/zZ7keQI5/XXX6/qpiIiSatSV8s45/YCefjn0neYWROAwPedgdWKgbSQzZoC26obVEREIhfJ1TKNAiN2zOxE4FLgE+AVYHhgteHA/MDjV4BBZlbXzJoBLYBVUc4d9NBDD/HQQw/FavciIp4Uyci9CbDUzD4ECvDPuS8AJgKXmdmnwGWB5zjn1gFzgfXAP4CRgWmdmFiyZAlLliyJ1e5FRDypwjl359yHQMcwy/cAvY+xzXhgfLXTiYhIlXj+E6oiIlKWiruISBLyfMvfBg0axDuCiEjC8Xxxf/HFF+MdQUQk4WhaRkQkCXm+uI8dO5axY8fGO4aISELx/LTMypUr4x1BRCTheH7kLiIiZam4i4gkIRV3EZEk5Pk596ZNm8Y7gohIwvF8cf/rX/8a7wgiIglH0zIiIknI88U9JyeHnJyceMcQEUkonp+WKSoqincEEZGE4/mRu4iIlBXJbfbSzGypmX1sZuvM7FeB5ePM7CszKwp89QvZZqyZbTKzDWbWJ5Y/gIiIlBXJtMxh4G7n3BozOwVYbWaLAq897pybFLqymbUGBgFtgLOAxWbWMpa32hMRkSNFcpu97cD2wON9ZvYxcHY5m/QHZjvnDgFfmNkmoDMQkyYwLVu2jMVuRUQ8rVInVM0sHf/9VN8DegCjzGwYUIh/dP81/sL/bshmxYT5ZWBm2UA2wDnnnFOV7ABMmzatytuKiCSriE+omtnJwItAjnPuW+BpoDngwz+yf6x01TCbuzILnJvmnMtwzmU0atSosrlFRKQcERV3M6uDv7DPcs69BOCc2+GcK3HO/QhMxz/1Av6RelrI5k2BbdGLfKTs7Gyys7NjtXsREU+K5GoZA/4EfOyc+0PI8iYhq10NrA08fgUYZGZ1zawZ0AJYFb3IR9q4cSMbN26M1e5FRDwpkjn3HsBQ4CMzKwosuxcYbGY+/FMum4FbAZxz68xsLrAe/5U2I3WljIhIzYrkapnlhJ9HX1jONuOB8dXIJSIi1aBPqIqIJCHP95bx+XzxjiAiknA8X9xzc3PjHUFEJOFoWkZEJAl5vrhff/31XH/99fGOISKSUDw/LVNcXBzvCCIiCcfzI3cRESlLxV1EJAmpuIuIJCHPz7l369Yt3hFERBKO54v7I488Eu8IIiIJR9MyIiJJyPPFfcCAAQwYMCDeMUREEornp2X27NkT7wgiIgnH8yN3EREpS8VdRCQJRXKbvTQzW2pmH5vZOjP7VWD56Wa2yMw+DXw/LWSbsWa2ycw2mFmfWP4AIiJSViRz7oeBu51za8zsFGC1mS0CRgBLnHMTzWwMMAa4x8xaA4OANsBZwGIzaxmrW+317t07FrsVEfG0SG6ztx3YHni8z8w+Bs4G+gNZgdWeBfKAewLLZzvnDgFfmNkmoDOwMtrhAf7nf/4nFrsVEfG0Ss25m1k60BF4DzgjUPhLfwE0Dqx2NrA1ZLPiwDIREakhERd3MzsZeBHIcc59W96qYZa5MPvLNrNCMyvctWtXpDHK6Nu3L3379q3y9iIiySii4m5mdfAX9lnOuZcCi3eYWZPA602AnYHlxUBayOZNgW1H79M5N805l+Gcy2jUqFFV8/P999/z/fffV3l7EZFkFMnVMgb8CfjYOfeHkJdeAYYHHg8H5ocsH2Rmdc2sGdACWBW9yCIiUpFIrpbpAQwFPjKzosCye4GJwFwzuwnYAlwD4JxbZ2ZzgfX4r7QZGasrZUREJLxIrpZZTvh5dICw1yE658YD46uRS0REqsHzvWWuuOKKeEcQEUk4ni/uv/nNb+IdQUQk4ai3jIhIEvJ8cc/KyiIrKyveMUREEorni7uIiJSl4i4ikoRU3EVEkpCKu4hIEvL8pZDXXnttvCOIiCQczxf3O+64I94RREQSjuenZQ4cOMCBAwfiHUNEJKF4fuTer18/APLy8uIbREQkgXh+5C4iImWpuIuIJCEVdxGRJKTiLiKShDx/QnXEiBHxjiAiknAiuYfqn81sp5mtDVk2zsy+MrOiwFe/kNfGmtkmM9tgZn1iFbzUiBEjVOBFRI4SybTMTODyMMsfd875Al8LAcysNTAIaBPYZoqZpUQrbDi7d+9m9+7dsTyEiIjnVFjcnXP5wL8i3F9/YLZz7pBz7gtgE9C5GvkqNHDgQAYOHBjLQ4iIeE51TqiOMrMPA9M2pwWWnQ1sDVmnOLCsDDPLNrNCMyvctWtXNWKIiMjRqlrcnwaaAz5gO/BYYLmFWdeF24FzbppzLsM5l9GoUaMqxhARkXCqVNydczuccyXOuR+B6fxn6qUYSAtZtSmwrXoRRUSksqpU3M2sScjTq4HSK2leAQaZWV0zawa0AFZVL6KIiFRWhde5m9kLQBbQ0MyKgQeALDPz4Z9y2QzcCuCcW2dmc4H1wGFgpHOuJCbJA26//fZY7l5ExJPMubBT4jUqIyPDFRYWxjuGiIinmNlq51xGuNc8335g69atbN26teIVRUSOI55vPzB06FBA/dxFREJ5fuQuIiJlqbiLiCQhFXcRkSSk4i4ikoQ8f0L17rvvjncEEZGE4/nifuWVV8Y7gohIwvH8tMyGDRvYsGFDvGOIiCQUz4/cb731VkDXuYuIhPL8yF1ERMpScRcRSUIq7iIiSUjFXUQkCXn+hOr9998f7wgiIgnH88X90ksvjXcEEZGEU+G0jJn92cx2mtnakGWnm9kiM/s08P20kNfGmtkmM9tgZn1iFbxUUVERRUVFsT6MiIinRDLnPhO4/KhlY4AlzrkWwJLAc8ysNTAIaBPYZoqZpUQtbRg5OTnk5OTE8hAiIp5TYXF3zuUD/zpqcX/g2cDjZ4GrQpbPds4dcs59AWwCOkcnqoiIRKqqV8uc4ZzbDhD43jiw/Gwg9J53xYFlZZhZtpkVmlnhrl27qhhDRETCifalkBZmWdg7cDvnpjnnMpxzGY0aNYpyDBGR41tVi/sOM2sCEPi+M7C8GEgLWa8psK3q8UREpCqqeinkK8BwYGLg+/yQ5c+b2R+As4AWwKrqhizPhAkTYrl7ERFPqrC4m9kLQBbQ0MyKgQfwF/W5ZnYTsAW4BsA5t87M5gLrgcPASOdcSYyyA9C9e/dY7l5ExJMqLO7OucHHeKn3MdYfD4yvTqjKWLFiBaAiLyISyvOfUL333nsB9XMXEQmlxmEiIklIxV1EJAmpuIuIJCEVdxGRJOT5E6q5ubnxjiAiknA8X9x9Pl+8I4iIJBzPT8ssXryYxYsXxzuGiEhC8fzI/eGHHwZ0RyYRkVCeH7mLiEhZKu4iIklIxV1EJAmpuIuIJCHPn1B95pln4h1BRCTheL64t2rVKt4RREQSjueL+6uvvsr897+iTbdLYnqcX1/WMqb7FxGJpmoVdzPbDOwDSoDDzrkMMzsdmAOkA5uBa51zX1cv5rE99thjFH/9fcyLu4iIl0TjhGov55zPOZcReD4GWOKcawEsCTwXEZEaFIurZfoDzwYePwtcFYNjiIhIOapb3B3wppmtNrPswLIznHPbAQLfG4fb0MyyzazQzAp37dpVzRgiIhKquidUezjntplZY2CRmX0S6YbOuWnANICMjAxXzRwiIhKiWsXdObct8H2nmb0MdAZ2mFkT59x2M2sC7IxCzmN67rnnmJ7/eSwPISLiOVWeljGzk8zslNLHwH8Ba4FXgOGB1YYD86sbsjxpaWmc1rhJLA8hIuI51ZlzPwNYbmYfAKuA15xz/wAmApeZ2afAZYHnMTNnzhzez1sYy0OIiHhOladlnHOfAx3CLN8D9K5OqMp4+umnKf76ezpm9aupQ4qIJDw1DhMRSUIq7iIiScjzvWVqyuOLNtbIcdTDRkSiQSN3EZEk5PmR+7x583g6b1O8Y4iIJBTPj9wbNmzIyfVPj3cMEZGE4vniPnPmTFa9+VK8Y4iIJBTPT8vMnDmT4q+/p/N//SLeUaKiJk7c6qStSPLz/MhdRETKUnEXEUlCnp+WkcrT1I9I8tPIXUQkCXl+5L5w4ULemzmWongHkSPoE70i8eX5kXu9evVIrVuHrlumxTuKiEjC8HxxnzJlCi8uLYp3DBGRhOL54j537lzeKtgQ7xgiIgnF83PucnzTlT8i4cWsuJvZ5cATQArwR+dcTG+3B9B1yzTePSc71ocRiTqdgJZoi0lxN7MU4Cn891AtBgrM7BXn3PpYHE9EJBa8/JdhrEbunYFNgfusYmazgf5AzIt76FUz0RzFH/1XQWX+SojmXxT666Tm1dSouiYk088i5TPnXPR3ajYQuNw5d3Pg+VCgi3NuVMg62UBplWoFVOesaENgdzW2rwnKGB1eyAjeyKmM0RHPjD91zjUK90KsRu4WZtkRv0Wcc9OAqFycbmaFzrmMaOwrVpQxOryQEbyRUxmjI1EzxupSyGIgLeR5U2BbjI4lIiJHiVVxLwBamFkzMzsBGAS8EqNjiYjIUWIyLeOcO2xmo4A38F8K+Wfn3LpYHCvAC70HlDE6vJARvJFTGaMjITPG5ISqiIjEl+fbD4iISFkq7iIiScgzxd3MLjezDWa2yczGhHndzGxy4PUPzeyCBMx4npmtNLNDZvabms4XkqOinEMC7+GHZrbCzDokYMb+gXxFZlZoZhclWsaQ9TqZWUng8x81KoL3McvMvgm8j0Vm9ruazhhJzsA6WYGM68zs7UTLaGajQ97HtYH/5qfXdM4g51zCf+E/KfsZcC5wAvAB0PqodfoBr+O/xr4r8F4CZmwMdALGA79J4PeyO3Ba4HHfBH0vT+Y/54zaA58kWsaQ9d4CFgIDEy0jkAUsiMf/i5XMeSr+T7ifE3jeONEyHrX+lcBb8XxfvTJyD7YzcM79GyhtZxCqP/AX5/cucKqZNUmkjM65nc65AuCHGsx1tEhyrnDOfR14+i7+zykkWsb9LvCvCDiJoz4klwgZA+4EXgR21mS4gEgzxlskOa8DXnLObQH/v6UEzBhqMPBCjSQ7Bq8U97OBrSHPiwPLKrtOLMX7+JGqbM6b8P9FVJMiymhmV5vZJ8BrwI01lK1UhRnN7GzgamBqDeYKFel/625m9oGZvW5mbWom2hEiydkSOM3M8sxstZkNq7F0fhH/uzGzesDl+H+px41X+rlX2M4gwnViKd7Hj1TEOc2sF/7iXtPz2RFldM69DLxsZpnAQ8ClsQ4WIpKMucA9zrkSs3Crx1wkGdfg70+y38z6AX8HWsQ62FEiyVkbuBDoDZwIrDSzd51zNdUJrTL/vq8E3nHO/SuGeSrkleIeSTuDeLc8iPfxIxVRTjNrD/wR6Ouc21ND2UpV6r10zuWbWXMza+icq6kGTpFkzABmBwp7Q6CfmR12zv29RhJGkNE5923I44VmNqWG30eI/N/3bufcd8B3ZpYPdABqqrhX5v/JQcR5SgbwzAnV2sDnQDP+czKjzVHr/JwjT6iuSrSMIeuOI34nVCN5L88BNgHdEzjjz/jPCdULgK9KnydKxqPWn0nNn1CN5H08M+R97Axsqcn3sRI5zweWBNatB6wF2iZSxsB69YF/ASfV5HsY7ssTI3d3jHYGZnZb4PWp+K9G6Ie/KB0Abki0jGZ2JlAI/AT40cxy8J9x//ZY+41HTuB3QANgSmDUedjVYNe7CDMOAIaZ2Q/A98AvXeBfVwJljKsIMw4Ebjezw/jfx0E1+T5GmtM597GZ/QP4EPgR/93d1iZSxsCqVwNvOv9fGHGl9gMiIknIK1fLiIhIJai4i4gkIRV3EZEkpOIuIpKEVNxFRJKQiruISBJScRcRSUL/H9hGxlBg9r2mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "flow_matrix = inflate(flow_matrix @ flow_matrix)\n",
    "compare_flow_distributions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This serves as the basis for a network clustering algorithm known as the **Markov Cluster Algorithm**. It is also referred to as **Markov clustering**, or **MCL** for short. MCL is executed by running `inflate(flow_matrix @ flow_matrix)` over many repeating iterations. We’ll now attempt to execute MCL. To start, we’ll run `flow_matrix = inflate(flow_matrix @ flow_matrix)` across 20 iterations.\n",
    "\n",
    "**Listing 19. 30 Inflating the product of `flow_matrix` repeatedly with itself**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "for _ in range(20):\n",
    "    flow_matrix = inflate(flow_matrix @ flow_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Certain edges in graph `G` should now have a flow of zero. We expect these edges to connect diverging counties. \n",
    "\n",
    "**Listing 19. 31 Selecting suspected inter-county edges**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We suspect 57 edges of appearing between counties.\n"
     ]
    }
   ],
   "source": [
    "suspected_inter_county = [(i, j) for (i, j) in G.edges()\n",
    "                         if not (flow_matrix[i][j] or flow_matrix[j][i])]\n",
    "num_suspected = len(suspected_inter_county)\n",
    "print(f\"We suspect {num_suspected} edges of appearing between counties.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deleting the suspected edges from our graph should sever all cross-county connections. Consequently, only clustered counties should remain if we visualize the graph after edge deletion.\n",
    "\n",
    "**Listing 19. 32 Deleting suspected inter-county edges**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "G_copy = G.copy()\n",
    "G_copy.remove_edges_from(suspected_inter_county)\n",
    "nx.draw(G_copy, with_labels=True, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All inter-county edges have been eliminated. Unfortunately, a few key intra-county edges have also been deleted. The problem is due to a minor error in our model. The model assumes that travelers can drive to neighboring towns, but it does not allow a traveller to remain in their current location. Adding self-loops to a graph will limit the unexpected model behaviour. Lets illustrate the impact of self-loops in a simple two-node adjacency matrix.\n",
    "\n",
    "**Listing 19. 33 Improving flow by adding self-loops**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The flow from A to B without self-loops is 0.0\n",
      "The flow from A to B with self-loops is 0.5\n"
     ]
    }
   ],
   "source": [
    "def compute_flow(adjacency_matrix):\n",
    "    transaction_matrix = adjacency_matrix / adjacency_matrix.sum(axis=0)\n",
    "    return (transaction_matrix @ transaction_matrix)[1][0]\n",
    "\n",
    "M1 = np.array([[0, 1], [1, 0]])\n",
    "M2 = np.array([[1, 1], [1, 1]])\n",
    "flow1, flow2 = [compute_flow(M) for M in [M1, M2]]\n",
    "print(f\"The flow from A to B without self-loops is {flow1}\")\n",
    "print(f\"The flow from A to B with self-loops is {flow2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding self-loops to graph `G` should limit inappropriate edge deletions. With this in mind, lets now define a `run_mcl` function.\n",
    "\n",
    "**Listing 19. 34 Defining an MCL function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def run_mcl(G):\n",
    "    for i in G.nodes:\n",
    "        G.add_edge(i, i)\n",
    "    \n",
    "    adjacency_matrix = nx.to_numpy_array(G)\n",
    "    transition_matrix = adjacency_matrix / adjacency_matrix.sum(axis=0)\n",
    "    flow_matrix = inflate(transition_matrix @ transition_matrix)\n",
    "    \n",
    "    for _ in range(20):\n",
    "        flow_matrix = inflate(flow_matrix @ flow_matrix)\n",
    "      \n",
    "    G.remove_edges_from([(i, j) for i, j in G.edges()\n",
    "                        if not (flow_matrix[i][j] or flow_matrix[j][i])])\n",
    "\n",
    "G_copy = G.copy()\n",
    "run_mcl(G_copy)\n",
    "nx.draw(G_copy, with_labels=True, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our graph has clustered perfectly into six secluded counties. In graph theory, such isolated clusters are referred to as **connected components**. In order to compute the full component of a node, it is sufficient to run `nx.shortest_path_length` on that node. The shortest path length algorithm will return only those nodes that are accessible within a clustered community. \n",
    "\n",
    "**Listing 19. 35 Using path lengths to uncover a county cluster**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The following towns are found in County 0:\n",
      "[0, 1, 2, 3, 4, 5, 6, 7]\n"
     ]
    }
   ],
   "source": [
    "component = nx.shortest_path_length(G_copy, source=0).keys()\n",
    "county_id = G.nodes[0]['county_id']\n",
    "for i in component:\n",
    "    assert G.nodes[i]['county_id'] == county_id\n",
    "    \n",
    "print(f\"The following towns are found in County {county_id}:\")\n",
    "print(sorted(component))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With minor modifications to the shortest path length algorithm, we can extract a graph’s connected components. This modified component algorithm is incorporated into NetworkX.\n",
    "\n",
    "**Listing 19. 36 Extracting all the clustered connected components**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The following towns are found in County 0:\n",
      "{0, 1, 2, 3, 4, 5, 6, 7}\n",
      "\n",
      "The following towns are found in County 1:\n",
      "{8, 9, 10, 11}\n",
      "\n",
      "The following towns are found in County 2:\n",
      "{12, 13, 14, 15, 16, 17}\n",
      "\n",
      "The following towns are found in County 3:\n",
      "{18, 19, 20}\n",
      "\n",
      "The following towns are found in County 4:\n",
      "{24, 21, 22, 23}\n",
      "\n",
      "The following towns are found in County 5:\n",
      "{25, 26, 27, 28, 29, 30}\n"
     ]
    }
   ],
   "source": [
    "for component in nx.connected_components(G_copy):\n",
    "    county_id = G.nodes[list(component)[0]]['county_id']\n",
    "    print(f\"\\nThe following towns are found in County {county_id}:\")\n",
    "    print(component)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our MCL implementation will not scale to very large networks. Further optimizations are required for successful scaling. These optimizations have been integrated into the external Markov Clustering library.\n",
    "\n",
    "**Listing 19. 37 Importing from the Markov Clustering library**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "from markov_clustering import get_clusters, run_mcl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given an adjacency matrix `M`, we can efficiently execute Markov clustering by running `get_clusters(run_mcl(M))`.\n",
    "\n",
    "**Listing 19. 38 Clustering with the Markov Clustering library**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The following towns are found in County 0:\n",
      "(0, 1, 2, 3, 4, 5, 6, 7)\n",
      "\n",
      "The following towns are found in County 1:\n",
      "(8, 9, 10, 11)\n",
      "\n",
      "The following towns are found in County 2:\n",
      "(12, 13, 14, 15, 16, 17)\n",
      "\n",
      "The following towns are found in County 3:\n",
      "(18, 19, 20)\n",
      "\n",
      "The following towns are found in County 4:\n",
      "(21, 22, 23, 24)\n",
      "\n",
      "The following towns are found in County 5:\n",
      "(25, 26, 27, 28, 29, 30)\n"
     ]
    }
   ],
   "source": [
    "adjacency_matrix = nx.to_numpy_array(G)\n",
    "clusters = get_clusters(run_mcl(adjacency_matrix))\n",
    "\n",
    "for cluster in clusters:\n",
    "    county_id = G.nodes[cluster[0]]['county_id']\n",
    "    print(f\"\\nThe following towns are found in County {county_id}:\")\n",
    "    print(cluster)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With Markov clustering, we can efficiently detect communities in community-structured graphs. This will prove useful when we search for groups of friends in social networks\n",
    "\n",
    "## 19. 4 Uncovering Friend Groups in Social Networks\n",
    "\n",
    "We can represent many processes as networks, including relationships between people. Within these **social networks**, nodes represent individual people. One famous social network is called _Zachery’s Karate Club_. That network can be loaded from NetworkX.\n",
    "\n",
    "**Listing 19. 39 Loading the Karate Club graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, {'club': 'Mr. Hi'}), (1, {'club': 'Mr. Hi'}), (2, {'club': 'Mr. Hi'}), (3, {'club': 'Mr. Hi'}), (4, {'club': 'Mr. Hi'}), (5, {'club': 'Mr. Hi'}), (6, {'club': 'Mr. Hi'}), (7, {'club': 'Mr. Hi'}), (8, {'club': 'Mr. Hi'}), (9, {'club': 'Officer'}), (10, {'club': 'Mr. Hi'}), (11, {'club': 'Mr. Hi'}), (12, {'club': 'Mr. Hi'}), (13, {'club': 'Mr. Hi'}), (14, {'club': 'Officer'}), (15, {'club': 'Officer'}), (16, {'club': 'Mr. Hi'}), (17, {'club': 'Mr. Hi'}), (18, {'club': 'Officer'}), (19, {'club': 'Mr. Hi'}), (20, {'club': 'Officer'}), (21, {'club': 'Mr. Hi'}), (22, {'club': 'Officer'}), (23, {'club': 'Officer'}), (24, {'club': 'Officer'}), (25, {'club': 'Officer'}), (26, {'club': 'Officer'}), (27, {'club': 'Officer'}), (28, {'club': 'Officer'}), (29, {'club': 'Officer'}), (30, {'club': 'Officer'}), (31, {'club': 'Officer'}), (32, {'club': 'Officer'}), (33, {'club': 'Officer'})]\n"
     ]
    }
   ],
   "source": [
    "G_karate = nx.karate_club_graph()\n",
    "print(G_karate.nodes(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our nodes track 34 people. Each node has a `club` attribute. That attribute is set to _Mr. Hi_ if the person joined Mr. Hi’s karate club. Otherwise, it’s set to _Officer_.  Lets go ahead and visualize the network.\n",
    "\n",
    "**Listing 19. 40 Visualizing the Karate Club graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "club_to_color = {'Mr. Hi': 'k', 'Officer': 'b'}\n",
    "node_colors = [club_to_color[G_karate.nodes[i]['club']] \n",
    "               for i in G_karate]\n",
    "\n",
    "nx.draw(G_karate, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Karate Club graph has a clear community structure. The colored clusters represent existing friend-groups. Lets extract these clusters using MCL.\n",
    "\n",
    "**Listing 19. 41 Clustering the Karate Club graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster 0:\n",
      "(0, 1, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 19, 21)\n",
      "\n",
      "Cluster 1:\n",
      "(2, 8, 9, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "adjacency_matrix = nx.to_numpy_array(G_karate)\n",
    "clusters = get_clusters(run_mcl(adjacency_matrix))\n",
    "for i, cluster in enumerate(clusters):\n",
    "    print(f\"Cluster {i}:\\n{cluster}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two clusters have been outputted as expected. We’ll now re-plot the graph, while coloring each node by cluster id.\n",
    "\n",
    "**Listing 19. 42 Coloring the plotted graph by cluster**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "cluster_0, cluster_1 = clusters\n",
    "node_colors = ['k' if i in cluster_0 else 'b'\n",
    "               for i in G_karate.nodes]\n",
    "\n",
    "nx.draw(G_karate, node_color=node_colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our clusters are nearly identical to the two splintered clubs. MCL has capably extracted the friend groups in the social network. The code below will illustrate how to color friend-groups in an automated manner.\n",
    "\n",
    "**Listing 19. 43 Coloring social graph clusters automatically**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "for cluster_id, node_indices in enumerate(clusters):\n",
    "    for i in node_indices:\n",
    "        G_karate.nodes[i]['cluster_id'] = cluster_id\n",
    "        \n",
    "node_colors = [G_karate.nodes[n]['cluster_id'] for n in G_karate.nodes]\n",
    "nx.draw(G_karate, node_color=node_colors, cmap=plt.cm.tab20)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
